In your case you have done an inter-cast marriage which false under special marriage act.1956 as per Law.
After that you did the Nikha as per Sharya law which abandon a Muslim to marry a Non-Muslim. If anyone wants to marry a Muslim person he/she has to accept and make faith in Islam & its principle. Else that marriage is haram (illegal) as per Sharya Law.
Now after your acceptance of Islam as your religion you should be known by your Islamic name however Islam does not put any pressure to anyone for the same you can keep your previous name and also can add your husband surname by using the marriage certificate.
Finally one advice that Islam is not only a religion it teaches the way to live life in disciplined way. So if you accept Islam as religion try to know it closely.
Best wishes for your future and married life.