Thayer sits next to 3 phonetic neighbors — Thatcher, Slater, and Draper are the closest matches by sound. Most share Thayer's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"army of the people, warrior of the nation"
"modern phonetic invention"
"from Saint-Denis"
"Yahweh remembers"
"playful one"
"permanent, long-lasting"
"son of Hutch (Hugh)"
"settlement by the fish dam"
"son of encouragement"
"an act of spiritual thanksgiving"
"God is gracious (from Shawn/Sean)"
"great chief, mighty lord"
"from the ash tree valley"
"hunter; huntsman"
"small deer"
"gift of God (folk etymology)"
"craftsman, smith"
"leopard, tiger (possible Arabic root)"
"friend of horses"
"God is my judge"
"the king"
Similar sound: These names share phonetic patterns with Thayer — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old German theod + hari origins, giving them the same cultural heritage as Thayer.
Rhythm: Thayer is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.