The question is whether it was really an email from Garmin, or rather from a hacker who stole so your access data in the hope that you also use Garmin Pay. I may be easily wrong, but I never heard that Garmin requires the real name for the account, never used it, and never got any email asking the change. And even if I got one, I would be extremely careful and in no case I would click any link on that email. If you did that, your original account may indeed have been stolen by a hacker.