Rhen sits next to 5 phonetic neighbors — Ren, Wren, and Rhett are the closest matches by sound. Most share Rhen's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"flowing river, running water"
"elm grove"
"may God protect"
"first, beginning"
"son of the pearl (via Margaret's meaning)"
"lasting, persistent"
"from 'deaglán', possibly 'good man'"
"rich in friends"
"from Vinci (a town in Tuscany)"
"man, free man"
"God gave"
"son of the sea, great tide"
"diminutive of Hobart"
"of the mountain"
"old friend, wise friend"
"battle spirit"
"from the rocky settlement"
"the greatest one, supreme ruler"
"World ruler (from Donald prefix Don-)"
"one who works with stored grain"
"slender, narrow"
Similar sound: These names share phonetic patterns with Rhen — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Celtic origins, giving them the same cultural heritage as Rhen.
Rhythm: Rhen is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.