Use the same process online name-generators use
I'm not sure of the protocol for providing answers that are pretty much just links to other answers on SE, but the answer to this worldbuilding question sounds like exactly what you're looking for.
tl;dr Define a set number of linguistic building blocks ('ne', 'rt', 's'en' etc.) and combine them using a random number generator. The set number of 'blocks' will help give your language a distinct 'sound' to it.
You can then go further by defining some grammatical rules like 'ab never follows aa' and cross out words that use that combination.
A point on real-world names
Names in the real world travel further than you think, even before the invention of fast travel and communication technologies. They travel by diffusion along shared borders, through shared history/mythology/religion, and through conquest.
Names that make the jump between cultures are frequently adapted to fit the vagarities of the adoptive language (or do so over time). This is one of the reasons the Hebrew name 'Yohanan' crops up as the Greek 'Ioannes', the Latin 'Johannus', the Slavic 'Ivan', the Arabic 'Yahya' the Italian 'Giovanni', the Spanish 'Juan', the French 'Jean', the German 'Hans', the Welsh 'Ifan', and the English 'John'.
Might be getting a little Worldbuilding.SE on you here, but if you use a couple of different iterations of your random name generator for different languages, you can use the interplay of your names to tell a little about the deeper history of your cultures. Who invaded who. Which religious movements spread through which cultures. Who has a shared mythological heritage, if not a linguistic one.
Pick one name, and morph its phonemes to fit each of your particular languages to paint a picture of a shared history.