Adding a name to a House deed

We are a gay Texas couple that has been together for 27 years. The house we've shared is paid for, but the title is in my partner's name. We have wills and power of attorney in each other's name. First, would it be wise to add my name to the deed of the house. Secondly, what (roughly) are the costs involved in transaction. Finally, since same-sex relationships are not recognized in Texas, will my name being added to the deed kick-in any type of gift taxes. Thank you.