Day sits next to 4 phonetic neighbors — Mae, Kay, and Ray are the closest matches by sound. Most share Day's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"daylight, brightness"
"precious, lovely (blend of Alana and Amanda influences)"
"little star, radiant one"
"gift of God"
"gift of God"
"born on Christmas Day"
"Bright and clear; variant of Serena"
Similar sound: These names share phonetic patterns with Day — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old English origins, giving them the same cultural heritage as Day.
Rhythm: Day is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.