The wrong name appears attached to my email. Somehow Mail thinks my email belongs to a different name
I think I found the problem -- I've seen this problem happen across 3 different macs in my extended family.  Today, in utter frustration, I started searching for a solution...

Previous Recipient list was not the problem.  It was Contacts.

Do a Spotlight search on your email address (the actually address) and see if you have extra contacts show up with that same email address.  In my case, I did.  Somehow Contacts was making all sorts of weird connections.

For instance, in my address book, "Prescott Police" had 7 (!) completely unrelated (and often obscure/hardly used) email addresses associated with it.

I edited the contact and deleted the extra email addresses associated with it.

I then stopped and restarted Mail, and the email address in question showed up with the correct name.

I have no idea how Contacts ended up making such strange associations, but so far I've been able to "fix" 2 errant names that I came across in the past 30 minutes.

I'm still on 10.10.5 (I never upgrade OS in the midst of a major project), and my mail services (IMAP) include Pair, iCloud, Gmail, and icdSoft.