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"
"heart, mind, spirit"
"son of the grey-haired one"
"bear, bear-like strength"
"From Hebrew 'Gavriel'; the archangel Gabriel appears in the Bible, ..."
"God is my power"
"blessed"
"son of the sea, great tide"
"lion"
"brave in war"
"gift of God"
"handsome; fair one"
"son of Jack"
"God is gracious"
"youthful, downy-bearded"
"God is gracious"
"son of Hendrik"
"flowing body of water, stream"
"soldier"
"handsome"
"great well"
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.