Thanks for the responses! Although there's plenty on here that have changed their last name, it looks like a significant majority kept theirs. Now I'll discuss what (IMO) the pros and cons of each are.
Pros of keeping your last name:
If your family is supportive, changing it might create unnecessary tension.
It may raise less scrutiny when you change your name, since the reason for changing your first and middle names is obvious but might wonder why you're also changing your last name.
No need to explain the difference in last name in family group settings, or on your birth certificate (assuming you can get it changed).
Pros of changing your last name:
If you have a family that's disowned you, it might feel good to make a break from them.
Stealth or partial stealth may be easier, as it often makes it harder for others to "connect the dots" between the old and new names if they see them together.
The reasons I asked separately about transwomen and transmen is I thought the former have a little more incentive to change their last name, since it's more normal for a woman to have used more than one last name since they frequently change them upon marriage or divorce. It also provides a way to bypass outing yourself if you're asked what your former name was and they don't have a
need to know in your case, since unless they ask for the full name you could say or put down just the former last name and they'd probably assume it was your "maiden" (or "previous married") name. (I got that idea from a transman who suggested putting down just your former initials on a job application if they're different, and I think for the MTF side my idea is an even better one. FTMs have the advantage in that they're less likely to be asked in a conversational setting about their former name since it's less likely that a man would've changed his name, while MTFs have the advantage of a way to respond without outing themselves but only if they've changed their last name.)
If you want to change your last name, but are worried about family reactions, a good compromise might be to pick a surname that was the maiden name of a recent ancestor (which keeps the family connection but is as good as changing to a random last name to non-family members).