The name Texas is a word for friendship that Europeans mistook for a name.
Wordorigins.org gives the source as the Caddo word táyšʔ, meaning "friend" or "ally." Texas Beyond History spells it taysha and agrees on the meaning. The Spanish applied it to the Hasinai Confederacy, a Caddo-speaking nation in what is now East Texas. Texas Beyond History says Spanish officials had heard of "the great kingdom of Tejas" before they met the Hasinai in the late 17th century. The final -s is the Spanish plural, so the name is a plural form.
The Spanish founded the Mission San Francisco de los Tejas near present-day Weches in 1690. The mission carried the name, and over time the label for a people stretched to cover their whole country.
English picked it up slowly. Wordorigins.org finds the earliest English use it knows in 1759, in a translation of Miguel Venegas's history of California. It uses the form "Los Tezas," a spelling not yet Anglicized. Jedidiah Morse's The American Gazetteer uses "Texas" in 1797, and the article says the name was fully Anglicized by the end of that century.
The meaning has been kept in public view. StateSymbolsUSA reports that Texas adopted "Friendship" as its state motto in 1930, through House Concurrent Resolution No. 22. The resolution links the name to the Indian word "Tejas," which it says means friendship. That source spells the Caddo word teyshas, so the spelling varies between sources (táyšʔ, taysha, teyshas), while the meaning stays the same.
The uncertain part is who first used the word for the region as a whole. The sources above do not say.