Legally in our country you are allowed to change your religion but not caste, however in your case you can contact religious authority/Leaders of caste you want to convert to, for having their acceptance. If you show your true desire they will accept you with your current caste.
You can have certain advantage if your caste name's spelling is similar to other caste For example
In Hindus Barai and Bari, Jat and jatav, yadav and jadhav
In Christianity Lannister and Lannistar
you can go for change of your name or correction in your legal identity but it will be illegal, I will not suggest it but its question of your marriage and you are true judge of your requirement and extent up to which you can go. If you are converting to caste which is under SC or ST, do not ever try to avail the reservation or concession, it will have legal consequences and you will land in trouble.