Yes she can change her name when becoming a USA citizen.My wife changed her name in the USA when became a citizen. She wanted to change her name here in the DR because she never liked her first name. The process has taken 2 years and lots of things to do in the process. So now she has the same name in both countries.
I know some foreign women married to Dominicans who have taken their husband's surnames, but none of the Dominicans I know, from all social backgrounds, do this any more. You might see it among the older generation, especially the upper classes.
To change names you can do it also being Dominican, its the same process and its long. Its not the same situation of using the husband lastname, in USa the wife can change it and take it as her first last name, here in Dominican Republic is added with "de" and for signing and in the oficial documents she will have 3 last names because she keeps their first 2 last names.
My wife's cedula has <her maidden name > de <my last name >
Her swiss passport only has my last name. When she changed her documents she said the swiss asked her if she wanted it the dr style, her maidden name or my name. *( i let her do that, serves her bloody right for being swiss ).
So basically her docs from the dr and from switzerland do not have the same name.