My first impulse is that the silent E is a feature of English phonology, so it applies mainly when the name comes via English (or French).
Ann = Anne, Carol = Carole, Lynn = Lynne, Fay = Faye
Wolf = Wolfe, Fox = Foxe, Clark = Clarke, Cook = Cooke, Sharp = Sharpe, Thick = Thicke, Fry = Frye, Hays = Hayes
Adding a silent E on the end may make the word look more old-fashioned, as in
Olde Englishe Shoppe
(In fact, because it's such a cliché, that particular name is now often pronounced humorously with the E's audible: Oldy Englishy Shoppy.)
Words imported from languages where we know the E is pronounced, however, usually retain some effort to pronounce it as a separate syllable, even if the vowel sound is altered to /i:/ (English long E).
adobe, tamale, abalone, coyote, guacamole, peyote
kamikaze, karate, karaoke, edamame, sake
linguine, finale, minestrone
In other cases, we may make a greater effort to approximate the original sound by altering it only to /e:j/ (English long A).
penne, andante, forte, sotto voce, al dente, latte
padre, hombre, mole (Mexican sauce), dengue (fever), merengue (dance)
When the original E is more like a schwa, it may sound more like an unstressed A in English and even come to be spelled with an A, as we associate A with the feminine via Latin.
Grete > Greta, Inge > Inga
lasagne > lasagna
chutzpah, shiksa, yenta
Not sure if any of that answers your question, but maybe it will help others think of other examples. (-: