Kaan sits next to 3 phonetic neighbors — Khan, Kane, and Jan are the closest matches by sound. Most share Kaan's Turkic-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"ruler, lord, king"
"the righteous ones, the pious"
"prince, commander (related form)"
"lion"
"the rightly guided one"
"leader, commander, chief"
"the khan, tribal chief"
"persevering, steadfast"
"father of many nations"
"vow to God, dedicated"
"man of peace"
"hero, valiant"
"benevolence, perfection of worship"
"trustworthy, reliable"
"joy, happiness"
Similar sound: These names share phonetic patterns with Kaan — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Turkic origins, giving them the same cultural heritage as Kaan.
Rhythm: Kaan is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.