Mails sent from my work gmail come back in my personal gmail
Ah, so this turns out to be a feature interaction issue.

Gmail always sends mail out with the address of the login of the SMTP account that sent it.

Mail will try multiple SMTP servers to send a mail if the first one fails.

So what was happening is that the settings for the SMTP on the work account were wrong, and the login failed. Mail silently failed over to the next server on the list, my home account. That login used my home address, so Gmail silently changed the name on the message.

Interesting.