In the century BCE we see a lot of people named Gaius and have weird names like Pompey or Sulla (tho I guess one of those is name Lucius, which is a name you can either pronounce in a christian way or a roman way) but then 100 or so years later (some later than others obviously) we start seeing names like Luke and Matthew.
Were names like Luke and Matthew around during the Roman Republic? If not, why did they start appearing soon after the fall of the Republic?
Maybe this is a huge topic too, but how prevalent was Judaism amongst the people of the Roman Republic? Was the prevalance of Judaism related to the changing preference in names in the Roman Empire?
First thing first: the Roman Republic fell at least 60 years before the historical Jesus preached.
Second: I think before we start we need a quick primer on Roman names. Classic Roman names had three parts. The first is the praenomen, which was drawn from a very limited set: Gaius, Sextus, Marcus, Quintus, etc. You'd have to know someone pretty well to use their praenomen. The second part is the nomen, or family name. This name identified your tribe. The final part was your cognomen, which loosely translates to "nickname".
So, you get "Marcus of the Tullii, called Chickpea", ie. Marcus Tullius Cicero, or "Gaius of the Julii, called 'The Hairy'"¹, ie. Gaius Julius Caesar.
This tripartite convention gets whittled down to two under the Empire, but the format is still roughly the same, with a given name and a family name. In this period, "Mark" and "Matthew" don't seem to be incredibly popular, and neither is "Luke", but there are quite a few "Johns". The prevalence of "Matthew" or "Matthias" (spelling irregularities make it difficult to differentiate in some cases) does increase later, and "John" remains fairly popular. "Bartholomew" and "Peter," as well as the occasional Old Testament names like "Simon" or "Solomon" do have occasional use as well, with "Peter" becoming particularly popular in the High Middle Ages.
However, in Late Antiquity, what replaces Roman names is not "Christian" ones, but Germanic names. Indeed, one of the ways we can trace the process of "Germanicization" in the west, or its inverse, Latin linguistic isolates, is through looking at personal names. We start seeing "Radbert", "Everard", "Henry", "Einhard", "Gotteschalk", "Hrabinus", etc.
It's only in the late Medieval and early Modern periods that a wide variety of New Testament names seem to really come to the fore.
¹Disputed etymology for "caesar".