Assuming you the mean spanish speaking countries rather than just Mexico, this thread has the answer you're looking for: the widespread use of Jesus as given name in Spain is linked to the similar popularity of the name Mohammed throughout the islamic world and more precisely during the started during the Moorish occupation of Spain.

I'd like to address an assumption in your title that I find to be incorrect: Jesus is a name that has received an enormous amount of versions, often completely orthographically and/or phonetically different depending on the language and culture who imported it. Many countries who have been under Christian influence still use descendants of those names today: Σωτήρης (Sotìris) is one such example in Greek, deriving from the word for Saviour, that is clearly attached to Jesus Christ; I'm uncertain of the commonness of the name Σωτήρης in Greece but other versions of it such as Salvador (Spanish) are even available to be found in toponymy (think of San Salvador), or such as Salvatore (Italian) are currently very common names (specifically it's an extremely common, "evergreen" name in southern Italy, especially Sicily, and it's quite common in names of Italian emigrants in other countries such as the USA as a result). Another common name that refers to Jesus is Joshua.

I would have been able to provide a very nice source on the spread of the name Salvatore in Italy but unfortunately it seems the page I was looking for (from one of Rome's universities, Tor Vergata) was lost and I can't locate it even with the Wayback Machine. The most reliable source I can provide is from the website of the national association of the Italian comuni, stating (in Italian, clearly) Salvatore as one of the most common names for newborns in Sicily: link; I can assure you, albeit anecdotally, that Salvatore is a very common name for any age range of males at least in Sicily.

Why do you think it is any more popular in Mexico than South America and Spain?