Lim sits next to 5 phonetic neighbors — Lin, Tim, and Kim are the closest matches by sound. Most share Lim's Chinese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"forest, grove of trees"
"beaver stream"
"to be strong"
"linden tree valley"
"widely known, celebrated, renowned"
"from the settlement at the ford"
"of the mountain"
"invented name combining bold 'Dray-' with '-vin' (poet, life)"
"free land, land without feudal obligation"
"one without bonds, free spirit"
"purple, royal dye"
"laurel, crown of victory"
"wine (joy) and peace combined"
Similar sound: These names share phonetic patterns with Lim — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Chinese origins, giving them the same cultural heritage as Lim.
Rhythm: Lim is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.