Q:

User with serial accounts; anything to be done? 

I just encountered a good answer:
https://diy.stackexchange.com/a/164858/27773
which was the first post by a new user (peter).  I thanked him for his good first answer, and he objected to my characterization of it as his first.  He says he has had "many" accounts; each time he's prompted for his username and password he registers again. 
I can't find any of his other accounts (there's no way to search by the username "peter"), and I have no evidence that he's doing any harm.  I am a bit ticked that he snitted at me for treating him as a newbie, but that's my problem, not SE's. 
Is there anything to be done here, or should I just continue to treat people as their profiles report? 
Edit: I've been corrected; you can search users by name, although it's a substring search; "peter" returns 300+ names. 

A:

I don't believe there's much to be done if they aren't causing any harm.  Should you see any abuse by users creating new accounts to conceal bad behavior, that would be appropriate to flag and we can address that. 
Your welcome messages to new users are nice for the site and I see no reason to refrain from that.  If someone wishes to remain relatively anonymous and create new accounts, they should be understanding that we will treat them as new users.  That's not SE's problem, or even yours, only the "new user".  They are welcome to register if this treatment bothers them and they want to be recognized as someone that isn't new to the site.