Dax sits next to 4 phonetic neighbors — Max, Zax, and Jax are the closest matches by sound. Most share Dax's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"water, thermal waters (place name)"
"thunder and lightning"
"narrow channel's son"
"ardor, enthusiasm, fierceness"
"slender, thin"
"defender, protector"
"king"
"valiant, brave"
"God's helper (ezer + El)"
"long hill, ridge"
"ruler of the people"
"bridge worker or keeper"
"beloved"
"hollow, empty"
"enthusiasm, ardent"
"measure, measurement tool"
"strife, war"
"leader, commander (variant interpretation)"
"glory of the land"
"statement of belief, system of faith"
"God is salvation, Yahweh saves"
Similar sound: These names share phonetic patterns with Dax — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have French/Basque origins, giving them the same cultural heritage as Dax.
Rhythm: Dax is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.