How did New Mexico get the name New Mexico?

Because it used to be part of Mexico, along with many other states in the U.S., so now it is called New Mexico. Yes, like all of the U.S. Southwest and Texas, New Mexico was part of Mexico until...

It was given to the area by the explorer and prospector Francisco de Ibarra in 1563 and became official when Juan de Onate was named the First Governor in 1598.

how did New Mexico get it's name

The first known use of the term Nuevo Mexico was in a 1563 report by explorer and prospector Francisco de Ibarra.

It became official when Juan de Onate was named the first Governor.