Coming out help (sort of)

Hi. At my new job I've made sure to apply with my preferred name because I thought I wouldn't get the position, but I ended up getting it (Yay!) I'm known by everyone with that name and have a visible nametag on my uniform. I work really close to home with my parents, so my mom mentioned she wants to drop in sometimes to say hi. Thats nice and all but I haven't told her about my preferred name and am worried one day she's going to pop in and be in a real shock because of it.

I don't know how to tell her about the name I use and am really scared of disappointing her. My older brother is trans and has been ostracized by my family because of it, and they had a real big fit about him changing his name. I can let my mom know about it because she was less unaccepting than my dad but just barely. I want to let her know that I use this name because I like it better and that i dont even want for her to refer to me by it. I just don't know how to phrase that without communicating to her that I have another name because I'm trans (even though that's why). Also my preferred name is nothing like my legal one and it's not nicknamey so I really can't think of a legitimate reason other than the truth, but i just want to give her a half truth basically if possible.

Any suggestions on how to parse this? Please help me 🙏