Question

What did Spain call Mexico during their reign?

Answer 1

The spanish called the mexico the new spain.
Mexico was colonized by the Spanish empire during that time. During this period, the Spanish Government requires all citizens to follow their regulations (such as they must speak spanish and they imposed conservative Christians as their nation's main religion). They do this in order to transform this whole new nation as a part of their own.

Answer 2

Mexico's name during Spain's reign was New Spain or Nueva España.