As someone who teaches some uni classes, I would like to say that if you cannot get your name changed on the official student list, don’t use only your nickname in emails or on assignments. You can for example put your nickname and then between brackets your official name. I have had students use completely different names than are in my records and it confuses the hell out of me when trying to figure out who exactly is contacting me
Sure, it's more practical if the student comes to you and tells you about it early on so that you can write it down in your own list and then go from there. Students usually add their student number and their last name to the signature too (or they should), so that makes it easier to track them down while allowing them to sign with the name by which they prefer to go.
It depends on the situation, I guess. If it's just carelessness on the student's part, and they didn't bother signing their e-mail at all or give you information on who they are/which class they belong to, it is super frustrating (though the university e-mail address should give you a bit of leeway there). However, asking a student to deadname themself in brackets for your own comfort, that's a hard no for me. If you do need to check because you don’t remember that name, their student number is just a CTRL+F away.