While "Natasha" is not an Arabic name, most probaby Russian or Ukranian, it can certainly be the name of a Muslim. In Islam, it is not necessary to change one's name when converting / reverting to Islam. To paraphrase William Shakespeare, "A Muslim by any other name, would be as sweet". The true sign of a Muslim is not just a name but his/her intentions and actions and their method of practising of the 5 pillars of Islam.
No, it's a Russian diminutive for the Latin name "Natalia".
"Natalia" means "birth", but the cultural connation is "birth of Christ", i.e., it's a name traditionally given to a child born at Christmas.
It is therefore a name that a strict Muslim would probably wish to avoid.
Natasha Braisewell's birth name is Natasha Kerllenevich.
Natasha Beaumont's birth name is Natasha Elisabeth Beaumont.
Natasha Saakas's birth name is Natasha Sakkas.
Natasha Etzer's birth name is Natasha Etzler.
Natasha Caraballo's birth name is Natasha Caraballo.
Natasha Cayman's birth name is Natasha Khawja.
Natasha Nov's birth name is Nova,Natasha.
Natasha Lannin's birth name is Natasha Michelle Lannin.
Natasha Collins's birth name is Natasha Louise Collins.
Natasha Richardson's birth name is Natasha Jane Richardson.
Natasha Ragsdale's birth name is Natasha Cristina Ragsdale.
Natasha Parnian's birth name is Natasha Soussan Parnian.