Yes, you can buy a home with your name only. However, Texas is a community property state, meaning it's owned together and I'm assuming that he'll live in the house as well.
I'm not an attorney and would highly suggest that you consult with one BEFORE purchasing a home if you'd want to keep the home for yourself if he leaves. Let me know if you need me to connect you with a local attorney or two. You can call me at 469-371-2899.
United Real Estate Dallas