what nationality is Abad, the people who have the name are irish and mexican decent

In Spanish it means "abbot."

J.R. is correct. It is a fairly common last name here in Guatemala.

I just came across this, which may be of interest.

The Greek Gospel of John says that Jesus named Simon as Kephas (Jn 1:42), and Paul used the Aramaic address to God, abba , even when writing to Greek-speaking Gentiles in Gal 4:6 and Rom 8:16. - Wikipedia