Taking on a Hebrew name?

[Mattityahu ben Noach]

Yes, a Noahide may do that if he/she wishes. Although a Noahide would normally retain his/her father's name, e.g. Iyov ben [son of] [his father's given names], unless there is a particular reason that the Noahide doesn't want to do so.

Suppose one's father wasn't particularly righteous, such that keeping his name alive be a reproach?
In Ezekiel 18 it says that if there is a son of a man who had sinned, and the son repents and removes himself from his father's sin, the sins of the son will not be remembered against him, and the chapter begins by assuring us that the sins of the father do not fall upon the son. Would it be better to put the past aside, and move forward (take a new name), or to keep mindful where one has come from to provide incentive not to return to that place?