Sketch of a more complete solution, excluding shortened forms and very foreign ones. Alternatives are in rough order of frequency.
vowel 0: E, Ye, Je, Ai. Optional and rare; Ai in particular is very rare.
consonant 1: C, K, G, Q. Mandatory; G and Q are rare.
vowel 1: a, aa, ai; optional h or gh. Mandatory. A few shortened forms use i instead.
consonant 2: t, tt, d. Almost mandatory, but a few r-centric variants lack it. There also seem to be a few
vowel 2: a, e. Optional, only valid if consonant 2 exists. In shortened forms, also i, ie, or y; this is the end.
consonant 3: r, l. Optional. Sometimes L starts a new word instead.
vowel 3: i, y, ee, ie, ii, e if no consonant 2, plus several rare vowel sequences. Almost mandatory (assuming consonant 3), but a few rare variants pack the r right next to the n.
consonant 4: n, nn, nh. Optional.
vowel 4: e, a, ey. Optional; ey is rare.
Some languages shove an s, c, x, t, k somewhere too (some of these are probably language-specific diminutives, but a few might be phoneme drift instead) ...
"Kaylee" and its variant "Kayla" should probably not be counted (despite almost fitting the pattern) since that's a compound of "Kay", adding the additional "Leigh" name.
