Legal Question in Business Law in Texas

Use of a name is really governed state by state. Texas would not check Florida to see if a name was available to be used as the name of an llc here. Far more important, however, is if the name is a name that has recognition in whatever trade the business is in and whether the owners of that business have taken steps to protect it from being used by someone else in the same field, for example if you could form coca cola, llc in Texas (which you can't) you would not be able to use the name.