Some Biblical names have vanished, presumably never to be seen again (Boaz). Some have been consistently popular throughout the ages (Elizabeth)
I actually know a little Boaz. So it hasn't disappeared altogether. Funnily enough, his sister is Elizabeth. Very Christian family.
I do think of Emily as a 'modern classic'. Alongside:
Amelia, Annabel, Charlotte, Daisy, Eleanor, Freya, Georgia, Isabella, Imogen, Jessica, Lucy, Madeleine, Matilda, Olivia, Phoebe, Sophia and Zara.
Some of those above were also classics in some of the 'non modern' lists of classics, I think. Including Emily, probably. But those are ones I think of as contemporary classics. Unlike 70s - 90s classics (Laura, Emma, Rebecca, Sarah) and 40s-60s classics (Susan, Pamela, Deborah, Jane, Anne).
I think only Elizabeth is a true classic in an 'always used' sense. Possibly Mary but not so much now.