Assalam u Alaykum My wife changed her last name to my last name. I didn't know that it was not required in Islam. Can she keep my last name or shall I change her last name back to her original last name before marriage? We both are born muslims Alhumdulillah.

All praise be to Allah. The norm in Islam is to be called after one’s father and one’s father ‘s family (while at the same time recognizing who one’s mother and mother’s side is.)

What is not allowed is to attribute oneself to someone who is not one’s father. That is why, in Islam, the wife continues to keep her maiden name so she is always attributed to her actual father and family. Therefore, it is best for a woman to keep her maiden name throughout her life, even after marriage. If, due to legal reasons for example, a woman does change her last name after marriage, it does not actual threaten her proper attribution as long as it is known in that society that she has now taken her husband’s name and she is not claiming attribution to what her new family name represents.  

In your particular case, if your wife does not need to keep your last name for any legal reasons and she has the means to change her name back to her maiden name, that would be best. If not and it is known that her last name is her husband’s name and not her family name, then her having her husband’s last name would probably not be forbidden. And Allah alone knows best.