Maxim sits next to 4 phonetic neighbors — Max, Maximus, and Maxwell are the closest matches by sound. Most share Maxim's Russian-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"greatest"
"of the Vergilii clan, flourishing"
"associated with luxury and elegance"
"god-helmet"
"free man, warrior"
"home ruler, lord of the house"
"tumult, noise"
"holy name, sacred name"
"bear"
"oak tree"
"bold bear"
"land power, territorial lord"
"rival, eager to excel"
"of the Antonius clan"
"from Percy (Norman place name)"
"brave spear, strong with a spear"
Similar sound: These names share phonetic patterns with Maxim — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Latin origins, giving them the same cultural heritage as Maxim.
Rhythm: Maxim is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.