Girls
Amity Josephine - Love love love. I actually think I just suggested this one today in the quick question thread. I adore Amity, the meaning, the sound, the fact that it feels wearable but is super uncommon, everything. It flows great with Josephine, which is a name I'm always iffy about because it feels old but sounds lovely. Overall, great combo, and I love the initials AJ, even though Amity is too cute to have a nickname.
Ava Kathryn - Not bad. I personally prefer Ada to Ava and Katherine to Katheryn, but since the differences are small I still like this combo overall. Good flow.
Clementine Eloise - I just can't get on the Clementine bandwagon, sorry. And there's something a bit off about the flow in this combo. But Eloise is pretty, I'm a sucker for El- names for girls.
Madeleine Anita - I really like Madeleine, particularly this spelling. I could take or leave Anita, and I don't think it flows that well as a middle here because it adds one too many N's. Madeleine Eloise would be really cute - it's still a tad off in flow but not that bad.
Margaret Rose - I'm iffy on Margaret. It seems a bit outdated to be but I think the nickname Maggie could really sell it, if you like that nickname. Rose is alright, I just feel like it's a super common middle and there are so many other flower names that you could use nowadays to modernize (if you want - I do like the idea of a flower name to freshen up Margaret). Some ideas: Margaret Lily, Margaret Iris, Margaret Poppy, Margaret Ivy, Margaret Clover.
Persphone Claire - I like this one. Persephone is kind of a GP of mine - I love mythology names, but most are difficult to picture on a real person, but I think Persephone could be pulled off (there's always nicknames like Peri/Perrie/Perry, Seph/Sephie, or even Pip). I like Claire, and it flows well with Persephone, which is difficult to pair with anything.
Boys
Edison Luis Miguel - I like the choice of Edison, because it brings famous scientist Thomas Edison to mind, and is a more interesting route to Eddy than traditional Edward/Edwin/etc. Luis and Miguel aren't bad as paired here, the flow is okay, but it does seem to be a bit of a mouthful.
Emory Maxwell - Love! I wouldn't think to use either of these names, but I really like them in this combo. I love uncommon E names for boys, and Emory is great. Maxwell is a handsome, classic choice that flows really well with Emory. Nice one!
Graham Chester Alan - I like Graham and I like Alan (although I prefer Allan or Allen, but I know sometimes people use family names or just have other preferences!) but I'm not a fan of Chester. The whole combo seems kind of clunky to me, whereas Emory Maxwell just flows right off the tongue without a second thought. Alan Graham would be nice, if you felt like switching things around and like Alan enough. other ideas: Graham Isaac, Graham Ezekiel, Graham Julian (although Julian Graham flows better - Graham is difficult to pair when in the first name slot), Vincent Graham, Simon Graham, Noah Graham, Nolan Graham/Graham Nolan.