As far as I know, neither Setup Assistant (which offers to migrate during initial setup) nor Migration Assistant (which you can run later) provides the ability to change the user name being migrated.
The best/easiest procedure probably depends on what data and/or settings you want to preserve from the old Mac... Regular files (documents)? Application preferences? Anything outside of his home directory?
(I'm assuming the old Mac is backed up to an external drive.)
I think the safest bet is to complete the set up of the new Mac with a new (admin) account for your mother.
After logging in to her (the only) account, I'd attach the backup drive, which by default will have "Ignore ownership on this volume" turned on. This gives her account the ability to copy any files wanted from the backup drive. You'd have to find all of the files you want to keep. When they are copied to the new Mac, the proper permissions will be set for the logged-in account (your mother's).
IF you want to migrate System Settings and Apps, then run Migration Assistant, but UN-check the old user account(s) so they won't be migrated. (You can do these two steps in either order.)
However, note that his procedure would not migrate preference settings for each app that your stepfather might have set up (in his account). Also, if there are apps which require license codes or something similar, they would have to be re-entered.
Alternatively, you could migrate his entire account during setup, and then try to change it to your mother's name later. The "Full Name" can easily be changed in System Settings. However, at least in Monterey, the GUI doesn't give you a way to change the name of the home folder itself within the filesystem (this matches the short name). You'd have to use Terminal commands to do so, and the 'dscl' command takes some experience, IMHO, and would be a little tricky. And I'm not sure what other gothca's might show up. It's likely possible, but...