There tends to be a 90-100 year rule with name popularity so right now there is a resurgence in names popular in the 1910s/20s. Therefore the next names to come through should be the ones from the 30s, think Ernest, Shirley, Brian, June, Joan, Betty, Ronald, Donald, Walter, Hilda, Audrey, Sylvia and Clifford.
Of course there is a lot of overlap with name popularity so we are already seeing little Olives, Dorothys, Evelyns, Irises and Florences as well as Stanleys, Sidneys, Erics, Arthurs and Alberts (all of these are in the current UK top 250 of their respective genders).
When it comes to the reports of names dying out completely, this is really rare. Yes, there are very few baby Garys or Paulas (26 Garys born in 2017 - slightly more if we could Gareths - and 46 Paulas born in that year) but for a name to truly 'die out' there needs to be no-one with that name alive at all (we are getting close with Fanny - there have been no baby Fannys registered in the last 23 years and hasn't been in the top 100 since 1904). Gary and Paula will come back round, probably in about 2040-2050 as they both peaking in around 1960.
So yes, we need to prepare ourselves for being introduced to grandchildren called Keith, Kenneth, Terrence and Trevor, and Patricia, Maureen, Sandra and Pamela....