It’s obvious that there is much, more more variability in names over the years, but this post from Baby Name Wizard quantifies this nicely:
In England in 1800, the top three names for boys and girls accounted for more than half of all babies born. That's despite a historically high fertility rate which made many parents dig deeper to name large families. Traditions to name after relatives and benefactors clarified choices even further. I think it's fair to speculate that the typical name-selection process of that time was a straightforward one.
By 1950 in the United States, you needed 79 names (through Gregory for boys, Paula for girls) to get the same population coverage that those six names achieved in England in 1800. Today, it would take 546 different names, including names like Raegan, Yaretzi, Jace and Heaven. And even those names barely scratch the surface of what's considered "normal." There is no longer any pre-defined set of acceptable names. That means there is no limit to your choices.
Does all this make things easier? Laura Wattenberg argues that it makes it harder for parents, and adds this final point: “brace yourself for the final kicker: both parents have to agree.”
This is one area in which it was probably easier to have restricted choice. It was certainly easier on those trying to figure out how to spell or pronounce some of the more creative names.