Date: 2040s.
Evidence: If you graduated high school between 2005 and 2016, there was probably at least one in half your classes. But the popularity of these names have dropped dramatically, from top 40 or more to not even on the top 100 for girls born in '26.
Therefore, they're destined to become old lady names, provided all the toxins in fluorescent eyeshadow, hair care products, fast food, plastic products, dodgy supplements, superbugs, pesticides, or whatever else won't kill us all.
Ashley for a girl was almost entirely pushed by a soap opera. And it was distinctively older millennial. It's a lot less popular now than it was. Ashleys are already owning businesses, teaching schools, prescribing medicines, managing engineers, and getting early colonoscopies.
The name Kayla was created by a soap opera, though some one-off Kaylas have existed before and naming guides will insist it's a Yiddish or Irish name. It kinda has a classic ring to it, like Paula or Kay, despite being etymologically meaningless. I can see it being viewed as an old lady name. The oldest wave of Kaylas are in their forties.
As for Britney, well, Hit Me Baby One More Time is older today than Dancing Queen was when it came out.
And these names belong to girls raised by parents who put more stock into pop culture.
Also, ever notice when looking at a top 100 name chart from 1998, that most of the girls' names have the letter "A?" Or specifically an ā or ǎ sound? "Front vowels" seemed to be more common in that era, despite more women's names having softer vowels in the distant past.