Maybe before you start, you could send emails to your teachers saying something like “[polite fluff] On your paper I’m listed as [legal name], but I use the name [new name], and my pronouns are [pronouns], and I’d like you to call me those things instead. [polite fluff]” Or you could go up to each teacher after/before class and say something similar. Here’s another template. Some teachers may be more amenable than others, and some may forget or “forget,” but it’s okay to ask. I did. Depending on where you live, it’s unlikely you’ll encounter outright hostility from your teachers in response, even if they don’t approve, but it’s always a possibility, and it’s something to be prepared for. There’s no “should,” as unhelpful as that is—it’s a decision you have to make for yourself, based on your situation and needs. Good luck!