[name]Hi[/name] there! I really love your choices of [name]Finnian[/name] and [name]Phoebe[/name], and I’m just so disappointed about darn [name]Phinneas[/name] and Ferb! 
I adore your combination, so it really saddens me to agree with you on being concerned to the point of finding new names. Granted, this is just my opinion, but it would really bother me, and I wouldn’t want to deal with any, “Oh! Like [name]Phinneas[/name] and Ferb!” comments. If you don’t mind those comments, should they arise, then by all means stick with the combination. But would it bother me? Yes, unfortunately.
For some odd reason, [name]Finnegan[/name] and [name]Phoebe[/name] doesn’t remind me of [name]Phinneas[/name] and Ferb. I guess the similar “nia” sound of [name]Finnian[/name] and [name]Phinneas[/name] is solved by choosing [name]Finnegan[/name], as the different ending distracts my brain. What to you think? Does [name]Finnegan[/name] solve the problem for you?
When it comes to deciding what to do, it all depends on which name you like more, [name]Finnian[/name] or [name]Phoebe[/name]. If your husband absolutely refuses to give up [name]Finnian[/name], then I guess poor [name]Phoebe[/name] is out the door. From what you wrote, it sounds like [name]Finnian[/name] will be staying, which is great, because it’s a wonderful name, and [name]Finn[/name] is a darling nickname.
I do like [name]Noah[/name], but I would never trade [name]Finnian[/name] for [name]Noah[/name]. I see that you like the names of Saints, so I’m wondering how you feel about [name]Elias[/name]. [name]Elias[/name] and [name]Phoebe[/name] would be great!
As for your little girl’s name, I personally wouldn’t name a baby [name]Delilah[/name], twin or not, because I simply can’t stop associating the name with the Biblical [name]Delilah[/name]. Plus, as you said, if you keep [name]Finnian[/name], you’d be naming one after a [name]Saint[/name], and the other, uh, not so much. 
[name]Rose[/name] is actually my favorite name in the world, so I’m behind it 100%! [name]Finn[/name] and [name]Rose[/name] sounds great, and [name]Rose[/name] is a [name]Saint[/name], too. I adore [name]Lila[/name], too, but love [name]Rose[/name] more, and while I do like [name]Felicity[/name] and [name]Faith[/name], I’m not a fan of matchy twin names. (Yes, [name]Finnian[/name] and [name]Phoebe[/name] is matchy, but I love it too much to care!)
If you were to keep [name]Phoebe[/name], some names other than [name]Noah[/name] you may like are:
[name]Phoebe[/name] and [name]Finnegan[/name] (see above)
[name]Phoebe[/name] and [name]Henry[/name]
[name]Phoebe[/name] and [name]Edward[/name] (nn [name]Teddy[/name])
[name]Phoebe[/name] and [name]Elias[/name]
[name]Phoebe[/name] and [name]Oliver[/name] (too cute!)
[name]Phoebe[/name] and [name]Miles[/name]
[name]Phoebe[/name] and [name]Milo[/name]
[name]Phoebe[/name] and [name]James[/name]
[name]Phoebe[/name] and [name]Charles[/name]
[name]Phoebe[/name] and [name]Peter[/name]
[name]Phoebe[/name] and [name]August[/name]/[name]Augustin[/name]
[name]Phoebe[/name] and [name]Leo[/name]
[name]Phoebe[/name] and [name]Simon[/name]
[name]Phoebe[/name] and [name]Lucas[/name]
[name]Phoebe[/name] and [name]Nicholas[/name]
[name]Phoebe[/name] and [name]William[/name]
If you want to keep [name]Finnian[/name] and aren’t set on [name]Rose[/name] or [name]Lila[/name], some other ideas include:
[name]Finnian[/name] and [name]Genevieve[/name] (plus, she’s a [name]Saint[/name], as are many of these names)
[name]Finnian[/name] and [name]Helena[/name]
[name]Finnian[/name] and [name]Lucy[/name]
[name]Finnian[/name] and [name]Georgia[/name]
[name]Finnian[/name] and [name]Beatrix[/name]
[name]Finnian[/name] and [name]Beatrice[/name]
[name]Finnian[/name] and [name]Annabelle[/name]
[name]Finnian[/name] and [name]Catherine[/name]
[name]Finnian[/name] and [name]Charlotte[/name]
[name]Finnian[/name] and [name]Cecilia[/name]/[name]Celia[/name]
[name]Finnian[/name] and [name]Josephine[/name] (you get the “f” sound in there, like with [name]Phoebe[/name])
[name]Finnian[/name] and [name]Emmeline[/name]
[name]Finnian[/name] and [name]Evangeline[/name]
[name]Finnian[/name] and [name]Delphine[/name] (f sound)
[name]Finnian[/name] and [name]Daphne[/name] (f sound)
[name]Finnian[/name] and [name]Sophie[/name] (f sound, but very popular)
[name]Finnian[/name] and [name]Eve[/name]
[name]Finnian[/name] and [name]Grace[/name]
[name]Finnian[/name] and [name]Hope[/name]
[name]Finnian[/name] and [name]Julia[/name]
[name]Finnian[/name] and [name]Juliet[/name]
[name]Finnian[/name] and [name]Kate[/name]
[name]Finnian[/name] and [name]Louisa[/name]
[name]Finnian[/name] and [name]Lydia[/name]
[name]Finnian[/name] and [name]Mariel[/name]
[name]Finnian[/name] and [name]Eleanor[/name]
[name]Finnian[/name] and [name]Susannah[/name]
[name]Finnian[/name] and [name]Violet[/name]
[name]Finnian[/name] and [name]Clementine[/name]
[name]Finnian[/name] and [name]Tess[/name]
[name]Finnian[/name] and [name]Blythe[/name]
[name]Finnian[/name] and [name]Claire[/name]
Of the names you listed, [name]Finnian[/name] and [name]Rose[/name] is my pick, followed by [name]Finnian[/name] and [name]Lila[/name]. If you keep [name]Phoebe[/name] and are still concerned which [name]Finnian[/name], I really do think [name]Finnegan[/name] would be a good substitute!
Best wishes to you!
Edited to add: I just remembered that [name]Jennifer[/name] Lopez named her twins [name]Max[/name] and [name]Emme[/name], the names of characters on Dragon Tales/Tails (I don’t remember which spelling the show uses). I’m by no means a J. Lo fan, but thought I’d let you know of someone who had a similar name issue, but chose to keep the names anyway.