Re: Nickname "Tex", real name...?
I don't know what Joel Madden naming his daughter Harlow has in common with an English person naming their kid Texas.
In the US, Texas is rarely if ever used as a full name. People who are given the nn Tex are given it because they are from Texas or seem like they are. Tex Ritter, for example. I don't know if he actually was from Texas, but he was a country-western singer so Tex fits with his image.
The only other famous Tex I can think of is Charles (Tex" Watson, one of Charles Manson's co-defendants. He really was from Texas. I'm willing to bet he wasn't called Tex while he lived in Texas.
In short, I think Tex is a silly name for somebody to be given at birth, regardless of where they're from.