I would think that changing the last name only should be fine though, since up until somewhat recently, most women changed their last names when they got married, so most systems should be equipped to handle this.

It used to be very common for migrants to change their surnames, although less so now. There used to be a person who wrote about Scottish Lithuanians called John Millar, who was born as Jonas Stepšys. Noam Chomsky had said that his family's surname was substantially altered after they went to the USA.