Thompson sits next to 4 phonetic neighbors — Thomson, Jackson, and Jameson are the closest matches by sound. Most share Thompson's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"son of Thomas, son of the twin"
"slender, powerful in battle"
"friend, darling"
"modern variant of Aeson (healer)"
"ancestor's descendant"
"supplanter"
"broad ford, wide river crossing"
"fortune, chance"
"healer"
"bent grass clearing"
"greatest, son of Max"
"from the badger settlement"
"goodness of God"
"lord of the sea"
"beam of light (via Ray)"
"remnants of a lake, driftwood"
"gift (modern American coinage)"
"peak, summit, apex"
"modern invented variant"
"who is like God"
"gift of God, gift of Yahweh"
Similar sound: These names share phonetic patterns with Thompson — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Middle English origins, giving them the same cultural heritage as Thompson.
Rhythm: Thompson is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.