A very uncommon name, it seems. Esai would seem to be a shortened form of Esaias, which is an older (in English) form of the Biblical prophet's name
Isaiah. The abbreviation for the Book of
Isaiah was often Esai. in older (16th-17th cent.) English texts.
I didn't see the form Esai occurring in Spanish texts of the Bible, but might have missed it.
- Da.