Dice sits next to 4 phonetic neighbors — Ice, Rice, and Nice are the closest matches by sound. Most share Dice's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"chance, fate, the throw"
"little rock, harmony"
"shining, pale"
"round, short person"
"to throw overboard, to cast away"
"resembling smoke, smoky in quality"
"wise, old power"
"The lord is high"
"undulating; like a wave"
"farm by the fen"
"modern invented name, phonetic blend"
Similar sound: These names share phonetic patterns with Dice — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin datum via Old French origins, giving them the same cultural heritage as Dice.
Rhythm: Dice is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.