Parker sits next to 3 phonetic neighbors — Porter, Paxer, and Barker are the closest matches by sound. Most share Parker's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"keeper of the game preserve"
"cart driver"
"God will uplift"
"Yahweh is God"
"well-born"
"bald, hairless"
"blazing iron"
"great king"
"son of Harry (Henry)"
"one who resembles God"
"supplanter, one who follows at the heel"
"twin"
"descendant of Aodh (fire)"
"supplanter"
"broad valley, broad hillside"
"gracious, dear, beloved"
"from the hollow"
"of uncertain origin, possibly barberry hill"
"happy, fortunate"
"house builder, craftsman"
Similar sound: These names share phonetic patterns with Parker — 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 Parker.
Rhythm: Parker is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.