Why are there relatively few personal names shared between Indo-European languages?

Brian is of course correct that naming simply isn’t as stable as, say, the Swadesh-100 list of core vocabulary, or for that matter syntax (VSO, SOV, SVO).

Things change much more quickly now than they used to, so you could object to Brian’s example. In English, the most popular names change radically every couple of decades; name fashions moved in a time scale of centuries in the 1500s. In Greece, where naming traditions were much more conservative until quite recently, names are specific to regions, and perpetuated from grandparent to grandchild. (Manuel is stereotypically Cretan, Athanasius is mainland.)

Christian names (not only from the Bible, but also names of saints) have of course also displaced other naming traditions to greater or lesser extents.

Well, writ large, you see change in naming tradition in the branches of Indo-European as well. Germanic, Greek and Indic share a naming tradition of compounds: Themistocles “glory of law”, Archimedes “counsel of leaders”. This is likely an Indo-European inheritance, and may or may not have been just for nobles. But there’s no trace of it in Latin.