I think names starting with B, D, F, J, M, N, P, R and T all seem to flow reasonably well (just due to positioning of tongue and palate - I'm a speech pathologist and I like to play with sounds - e.g. c, g, k and q are all back of the throat sounds so to use them after you've just made an x sound seems to be a bit much to me - my technical but completely personal opinion)
And I'm not a fan of middle names starting with vowels after Axel just because it starts to remind me of the word axolotl (one of those walking fish/lizard things).
E.gs from those letters: Axel Bryce, Axel Dreydon, Axel Flynn, Axel James, Axel Mason, Axel Nathan, Axel Perry, Axel Rhett, Axel Tristan...
Axel Edison
Axel James
Axel Ryan
James Alex
Matthew Alex
John Alex
Benjamin Alex
Jamison Alex
Jason Alex
Edison Alex
Johnathan Alex
Rose, Foley?? Haha jk how about Michael or David, or Wyatt