Verbally, I just give up and clearly write my name down in block letters and hand the slip of paper over to the employee. Until they get to know you, expect to show your tourist card, plus a picture I.D. as verification. It makes picking up the mail a little more exciting. The post office will not accept anything but Mexican pesos. Mail is generally held for two weeks.
Unclaimed letters have an excellent chance of making it back to the sender.
If you are in need of stationery, you'll need to find a papeleria. All villages of any note usually have one or two tiny papelerias. Mexico's infrastructure isn't set up to do really rapid delivery of mail or parcels. In an emergency, I'd travel to a city with a major international airport, and make arrangements to pick up the parcel at the Fed Ex counter. Note, every article entering Mexico is subject to tariff duties if applicable.