I want to use my dad last name which is Partee is it illegal to use it if my name is not changed to this

It is perfectly legal to use any name you want, as long as you are not doing it for purposes of defrauding someone.  As long as you are not using another name to avoid creditors or the police, or to try to collect someone else's benefits or cash their checks, or for some other nefarious purpose, you should have no problem.