There are very few genuinely timeless names, where you can't accurately guess the age of the owner. Here in the UK 'royal names' probably come closest - things like Catherine, Elizabeth, Charlotte, Eleanor and Alice for girls, WIlliam, Henry, James and George for boys.
Agree with the cyclical/100 year thing, but I think you also get particular 'sound trends', where names that have a particular style or group of letters suddenly get popular. E.g. lots of people begin to choose Emily, next people might see Emily as too popular and plump for Amelia instead, then the trend moves on to include alternative spellings/versions e.g. Emilie, Emilia, Amelie as people look for 'something a bit different', and finally the trend broadens out to include names with a similar 'feel'. e.g. from Emily to Amelie to Elodie.
Recently we've had the nicknamey 'ee sound' trend for both sexes (Ellie/Lily/Milly/Tilly/Maisie; Alfie/Archie/Freddie/Charlie), the Latinate trend for girls (Olivia, Amelia, Sophia, Isabella) and Old Testament names for boys (Noah, Isaac, Joshua, Jacob). There's also a bit of a current fashion for names ending in -o, hence the rise of Arlo. Think it might have started with Leo and then Milo (Tweenies?) a few years back.
I predict mid-century/Enid Blyton names will start to make a comeback soon - things like Anne, Nancy, Susan, Daphne, Hazel, Sally for girls and Peter, Robin, Philip, Ralph and Laurence for boys.