I was released from cdcr about 4 months ago my wife is still inside and I'm wondering how difficult it is to get correspondence approval even though we're not legally married

This one is a slippery slope. The correct way of going about it is to ask for permission from your wife's warden or even your probation officer (assuming you are on paper now). If they will not grant it, you risk re-offending by going around the rules like using a different name... if they catch on, it'll be a problem for you both.