A word with one syllable is "monosyllabic". Two syllables is "disyllabic", three is "trisyllabic", and so on. "Polysyllabic" refers to any word with more than one syllable. Is there any single term for words that have more than two (including three, four, five, and so on)?
According to Merriam-Webster's Dictionary:
: having more than one and usually more than three syllables :
// a multisyllabic word
Since you don't show an example case it's hard to tell if this is appropriate, but if your requirement is for a minimum of three, then "3+ syllables" might fit the bill.