If the sole reason for not using your real name is to protect him, fuck no. Let your name fly free.
If you truly fear for your safety, then please be safe.
If you intend to really keep your name (legally), I say use it, be proud of it, shout it from the hill. Who knows maybe calling out who the abuser by his full name is a proper response so other women can be protected from this evil and vile person.
Be well, be safe, and be proud that you are strong.