Far from being "stolen," those names (in the case of the states you mention) were given when North America was colonized by Europeans, by the Europeans who settled in them...and were actually mandated by the Crown, in some cases. The English were not the only European power to colonize North America...the Spanish, the French, and the Dutch all claimed territories in North America. Those territories eventually became the United States of America. The Spanish territories were the longest to endure, existing long after the American Revolution. Texas was a province of colonial Mexico, a colony of Spain, as was (surprise) New Mexico. In the case of Texas (Tejas), native Tejanos (the Mexican provincial settlers of Texas) allied with American settlers and pioneers in a bid for independence from Mexico. Sam Houston led a ragtag army against the Mexican army dispatched to deal with the rebellious province. As history tells, Texas won its independence from Mexico, but ended up being wooed by the US federal government into statehood, which ended a brief existence as an independent Republic.
You should also be aware that the US is comprised of immigrants from all over the globe. It was customary for groups of immigrants, upon settling in an area, to name their settlement after a city or region from their country of origin.
In a nutshell, the "stolen" place names are in fact signs of the influence other nations have had on the USA. Louisiana is a great example. The organization of that state harkens back to the days when it was alternatively under French and Spanish control. Baton Rouge, New Orleans, etc...and the "Parishes" instead of counties as you find in other states. In the past, these places were under the direct control of another country. I would consider that as you ponder this issue.
EDIT - By the way, Texas has a rather colorful and fascinating history that makes for a good read. There are a number of books out there on the subject. One of the best is a book that delves into the personalities of both Sam Houston and Santa Anna, titled
The Eagle and the Raven. It's amazing just how closely related their life histories are. Both were eccentric and flamboyant, charismatic, and just a wee bit egotistical.

History doesn't treat Santa Anna very well...while it's true he was utterly incapable as a statesman, he was a fearless military leader who was actually quite accomplished on the battlefield. Sam Houston was a washed-up American politician who made his way to Texas like many other native Tennesseans did in those days (David Crockett was another). He was a misfit who generally despised society, and was known to disappear for months at a time, going to live with tribes of native Americans he knew well. Perhaps his time spent with these tribes gave him an advantage when he led the relatively pitiful Texas army against the well-supplied and larger Mexican force led by Santa Anna. He basically spent his time running away from conflict with the Mexican army, until the right opportunity presented itself to attack...and that is history, as he caught the Mexican army literally with their pants down.
