Texas name changes go through the courts from my understanding. If you are a cis person getting a normal cis name change, it's probably no problem. I know someone who had their first and last named changed.
If you are a trans, then it's more dependent on what judge you get I think? But if you are going with normal gender neutral names, it's probably not a big deal. I haven't looked that much into it since the biggest hurdle for me would be finding a name I want. If you have a criminal history it'll also probably complicate the process.