Rhyne sits next to 4 phonetic neighbors — Rhine, Ryan, and Ryne are the closest matches by sound. Most share Rhyne's German-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"dweller by the Rhine river"
"the metal iron, element of strength and endurance"
"Virtuous, worthy, able"
"coined American name; no classical etymology"
"sun of the faith, sun of religion"
"angel, divine messenger"
"already; already seen"
"great, majestic"
"devoted to Demeter, goddess of harvest"
"stream, rivulet, small river"
Similar sound: These names share phonetic patterns with Rhyne — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have German origins, giving them the same cultural heritage as Rhyne.
Rhythm: Rhyne is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.