Complaint sub-issue: Personal information incorrect

I will attempt to make a very long story short. To begin, it is important to know that I am in the process of qualifying for a loan. My loan officer was able to successfully pull my credit information from XXXX and XXXX ( no problems at all ), but was unable to get this information from Equifax. They advised me to call and provide them with my information so they can verify my identity or, at the very least, get additional information as to why my information can not be accessed by my loan officer. I call in around late XXXX and the woman I spoke to states that they can not find a profile with the information I have provided. Very odd, as I know that I have provided her with all my correct information ( Full Name, Social Security Number, Address, etc. ). She advised that I send in a cover letter that includes my full name, address, phone number, and essentially an explanation/summary as to why I was sending this information in. She also advised I send in a copy of my ID and of my Social Security Card to Equifax at XXXX XXXX XXXX XXXX GA XXXX or fax it to XXXX. My loan application was put on hold and a few months went by. On XX/XX/2019, I faxed in and mailed the aforementioned information to resolve this issue. I then called XXXX about a week later and the woman on the line asked for all of my information and confirmed she can not find a file with my information. I told her that this was exactly why I was calling and was hoping to confirm that the information I submitted via fax and mail was received. She stated they did not have these documents on file as of yet, could not give me additional information, and to wait until I receive a confirmation letter in the mail. She stated this letter could take up to a month to reach me. I was not happy about the time frame she gave me but understood that there was a process they need to follow ( hopefully to protect my information ). I waited. And waited. Nothing came in the mail. On XX/XX/2019, I called in to Equifax again to check on the status of my " dispute. '' I was essentially told by XXXX that they they have still not received my information ( as it has not been uploaded to my account ) and to send it in again. I asked if it typically takes this long to process the fax/mail and to upload it to my account. He stated that faxes are typically processes in 3-5 business days and mailed in information may  take up to 30 days to be processed and uploaded. This made me think that they never received my information or lost it since it had been a month since I sent this information in. XXXX then stated that I should contact my bank to confirm that they have my information correctly. Essentially, he said that my bank may not be reporting my credit information to Equifax. I told him this is unlikely because the other two credit bureaus have their information on file, but told him I would call to make sure and send in my information again. I confirmed that I need to send it in to XXXX XXXX XXXX XXXX GA XXXX and fax it to XXXX ; he stated that was correct. 
On XX/XX/2019, I called my local bank, spoke with XXXX ( who was very kind and helpful ), and she confirmed that they report credit cards to all three bureaus. She suggested I call the number on my credit card in order to confirm that my bank has my information correctly listed. I did so, explained the situation to a woman named XXXX, and was transferred to my bank 's credit bureau team. It was here that I spoke to XXXX ( also very helpful ), who also confirmed that they report credit information to all 3 bureaus on a monthly basis. XXXX also verified my name, address, date of birth, and social security number ; I confirmed that all of this information is correct on their end. XXXX offered to send my information to her maintenance team, who will reach out to Equifax on my behalf and hopefully get additional information from them/resolve the issue. 
On XX/XX/2019, XXXX called me and left a voicemail requesting I call her back as soon as possible. When I did so, I was connected with XXXX who stated XXXX was on another call but had made detailed notes on my account regarding Equifax. Essentially, XXXX told me that Equifax has a different name associated with my social security number. I asked if it could be a variant of my name, but XXXX stated that variants are typically resolved quickly so this may be a completely different name ; they told her to have me send in my social security information and ID once again. Okay, so now I'm thinking that Equifax has a completely different person associated with my Social Security number. Obviously that is very concerning. 
After this call from my bank, I fax and mail an updated cover letter, my social security card, my passport, and the receipt of my previous fax on XXXX to Equifax. 
I called Equifax again on this date to let them know that I had done so and to let them know what my bank had told me. I spoke with XXXX, who told me to wait 30 days to receive confirmation response in mail. I told her that I had also sent this information on XXXX and asked her to see if that was ever received. She stated it was not uploaded to my account so was never received. I let her know that this does not make me feel confident they will receive my information this time, as it was sent to the same fax and address. XXXX told me to call back in 3-5 business days as this is typically how long it takes to process a fax. I told her I will do that. 
I called back on XX/XX/2019. The person I spoke to stated they did not receive any documents and nothing has been uploaded to my account. I asked to speak to a supervisor and XXXX picked up my call. XXXX stated that it takes 5-7 business days to process a fax ; I let him know that his team members have not given me that time frame, and are therefore giving out incorrect information. He stated there is nothing he can do until they receive my information and suggested I send it in a third time. At this point, I am flustered because I have been given conflicting information and they never received my fax or mail the first time I sent it in. 
I call again on XX/XX/XXXX, and the woman I spoke t stated they have received my information via fax and I should receive a written confirmation in the mail regarding this dispute in a few days. I check my mail and see that I have two " confirmation '' letter from Equifax. One is dated XX/XX/XXXX and does not have my complete name listed ; this one is six pages long and states that the " information you disputed has been updated as well as other information on this item. '' Very vague. It then goes on to state that the " information you disputed has been verified as accurate, however, information unrelated to your dispute has been undated. '' What exactly does that mean? 
The second confirmation letter is dated for XX/XX/2019. This letter also states the " information you disputed has been updated as well as other information on this item, '' but goes on to state that my name has been updated. Initially I thought this was great news because they have updated my name in the system to match the information I provided, not some other person 's random information. Unfortunately, I take a closer look at the name they have updated my information to, and realize my last name is misspelled. I have no idea why they have updated my last name to this incorrect spelling, especially since they have my Social Security card and ID with the correct spelling of my name. 
I called Equifax on XX/XX/2019 to ask for clarification and ask them why they updated my name to this random spelling. I never asked for them to update my name ; I had sent in my information so they can confirm my identity and find my credit profile ( to see what information they had incorrectly in their system ). I initially spoke with XXXX, who told me that they are having a system update and to call back in an hour. 
When I did, I spoke with XXXX and told him my name has been updated to an incorrect spelling and I have the confirmation number if he needs it. XXXX did not ask for this confirmation number, asked for my information, and then stated he can not proceed with this claim because they do not have enough information to verify my identity. I asked dhow this was possible as I have sent in my information twice and was told it was received, and received not one but two confirmation letters. XXXX stated there is nothing he can do, there are not documents associated with my account, and I need to send it in again. I am very frustrated now and disconnect the call. 
Later, I call in again. There must be some mistake. I am connected with XXXX and immediately ask for a supervisor. She refused so I give her the entire story. I am put on hold and XXXX states the same thing that XXXX did ; they do not have information on file for me and I need to send it in again. I refuse and ask her to look for it again as it has been confirmed as received in the past. I am place on hold and XXXX now states she has found the documents I have been referring to, has me confirm the spelling of my name and does spell back my name incorrectly. This confirms they have updated my name incorrectly. I was placed on hold a third time and XXXX tells me I should wait for the confirmation letter. One again, I reiterate to her that I have received these confirmation letters and they do not make sense ; my name has been updated incorrectly. I ask if there is any other way we can resolve this issue because I am not willing to send in my information again, as I have done so and for some reason they decided to update my name incorrectly. Again, I am put on hold and XXXX states she can't verify my identity by asking verification questions because there is no credit information associated with my profile. I say of course there is not because that profile has an incorrect spelling of my name, and who knew who was associated with my social previously/how it was spelled before. I ask for the supervisor again and am transferred to XXXX again. After giving him the spiel once again, XXXX stated he will place me on hold and try to get a hold of their Office of Consumer Affairs. Once back on the line, he states that office is not open but I simply need to send m information again to get this resolved ; XXXX states I don't need to call in to get this resolved. I let XXXX know that, with all due respect, I do no have confidence it is that simple considering all that has happened. I asked him if he will call them again when they are open on my behalf to get this resolved. He stated he will not. I told him, in that case, I definitely need to keep calling and will call Equifax again tomorrow when that office is open and they can call them on my behalf while I am on the line if they will not do so otherwise to resolve this issue. Then we can talk about sending my information a third time.