The dynamics of Jeffrey seem quite similar, peaking at ~15 ‰ between 1961 and 1971 (versus ~4 ‰ for Jeffery and Jeff). So perhaps the question is worth extending to all variants of the name (though Geoffrey seems a lot less popular and peaked later cca 1975 at less than 1‰).

It's quite possible that the Jeff(r)(e)ys got their boost from renewed interest in a comic strip. The syndicated strip Mutt and Jeff had been around since 1907, but received a boost when President Eisenhower raved about the strip at a White House breakfast for the National Cartoonist Society. Mentioned here.

Classic Mutt and Jeff strips are still available from GoComics

Looking at the chart for Jeffrey, it looks like there was an initial spike in popularity in the late 1930s to early 1940s. It's possible there was a popular radio show with an actor or character by that name.

Given that Geoffrey, Jeffery, and Jeffrey are all basically the same name and given the wide variety of name spellings back then? It's plausible that something caused that initial spike and it sort of snow-balled from there across multiple spellings. As for why Geoffrey never got quite as popular as Jeffrey/Jeffery? Possible because the soft-G in that spelling is seen as a British thing? Like spelling color like colour with in extraneous u?