I've made a generator to make plausible names for American characters based on their decade of birth.

perchance.org/us-names

You can pick any decade from the 1920s to the 2010s, and get it to generate a forename or a full name for a man or a woman born in that decade. There's also a surname generator based on 2010 data. Unlike a lot of name generators, it doesn't simply pick from a list of equally likely choices, the chances are weighted.

The forenames are chosen from the 200 most popular forenames for people born in that decade (according to the Social Security Administration), weighted by their relative popularity. So for the 2010 girls, for example, Emma (the most popular name) is 12 times more likely to be picked than Izabella (the 200th).

Similarly, the surnames are the most common 1000 surnames from the 2010 census, weighted for popularity from Smith to the 70-times-less-common Archer.

No attempt is made to match asian or hispanic forenames and surnames, so you can still get some fairly unlikely combinations, but it may help stem the endless tide of Elaras and Rachels.

Use it as-is to generate a name for a character manually, or incorporate it into your own generators. There are separate lists for male and female forenames or for full names for each decade, and one for the surnames, all documented on the generator's page.

I hope people find this useful. I'd love to see it added to the list of useful generators.