Ah, the good old days, where everyone in the neighborhood had kids named John and Mary (or Juan and Maria, or Jean and Marie, etc). But all of the warm fuzzy melting pot of same-name-ness started to disintegrate in the 1960s, when diversification of baby names started in the US, "at the same time that Americans started placing more emphasis on individuality and less on collectivity and fitting in," according to the Live Science article.1

Enter the Social Security Administration, Shannon entropy, and kids ending up with names like Apple and Pilot Inspektor.2 Recently the SSA started publishing statistics on baby names, so author Laura Wattenberg, who had seemingly little else to do, analyzed the statistics and came up with a measure of called Shannon entropy. The measure "is used to describe the information contained in a message - in this case, how much is communicated by the choice of a name."
Wattenberg calculated a sharp rise in name entropy over time. She found that this measure of the information carried by names has risen as much in the past 25 years as it did in the full century before that. (The measure is independent of the number of babies born.)

That means that meeting a baby named Mary today tells you a lot more about the girl's parents than meeting a baby with the same name 50 years ago would have. And the same goes for any name you can think of.

Names communicate so much, because they often embody parents' values and tastes, as well as dreams and ambitions for their child.
I love the quote by Jean Twenge, a professor of psychology at San Diego State University, about the research. She called Wattenberg's work an "interesting analysis" and said, "It looks solid to me."

Wattenberg says the data have had a "huge effect. ... "There's a kind of reverse competitiveness that nobody wants to be number one."

And as much as people strive for uniqueness, ultimately humans are social animals that still want to fit in.

"We all want to be different from each other, but our tastes are still as much alike as they ever were," Wattenberg said. "So the result is we have a thousand tiny variations on a theme. You get Kayden, Brayden, Hayden, Jayden."
On the downside, kids need to dig deeper to make puns on names nowadays. Maybe one day a creative parent will come up with a name that rhymes with orange or whilst or depth and we can check those off the words without rhymes list.

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1 I still don't think that explains Bunny or Candy or other stripper-esque names, but to each his own.
2 Sadly, I've heard worse - a friend of mine is a teacher and shares names that are actually unbelievable - as in, I can't believe a parent would be that high or delusional to name their kid that.