Now I really don't get it.
If myname.com is your domain, that you have registered at some domain registrar, and the registration hasn't expired, then how is it related to that MS account. If the NS records for your domain do not point to MS then hacking your old MS account cannot host email for your domain.
If the email address
myemail@myname.com was used as the username for that MS account, with some password that has been forgotten, then replacing it with
scammersemail@scammer.com will probably break any connection between that account and your domain.
I don't understand what is the "security info for
myemail@myname.com" that is being replaced, and how it can be replaced with some other email address if it is the "security info" for a particular address.
This message form MS is quite uninformative about what's really happening.