Shaz sits next to 4 phonetic neighbors — Shay, Raz, and Jaz are the closest matches by sound. Most share Shaz's Hebrew via English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"diminutive of Sharon (fertile plain)"
"the day (personified deity)"
"desired, longed for"
"from the hill settlement, dweller by the downs"
"divine law, path to the watering hole"
"Little fire (as variant of Aidan)"
"Armenian (the people)"
"eagle of Thor"
"iron strength"
"sudden dash or rush"
"Just; upright; righteous"
"from the white meadow"
"highest point, peak, summit"
"God has grasped"
Similar sound: These names share phonetic patterns with Shaz — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Hebrew via English origins, giving them the same cultural heritage as Shaz.
Rhythm: Shaz is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.