Pugmire rhymes with:
stegemeier, biedermeier, dannemeyer, fesmire, foxmeyer, hehmeyer, jurgensmeyer, kastenmeier, obermaier, ohlmeyer, proxmire, racamier, retemeyer, rightmire, rothmeier, settlemire, settlemyre, stegemeier, stiegemeier, stoudemire, stoudenmire, suttmeier, tietmeyer, untermeyer, waymire, whitmire
Pugmire sounds like:
passmore, pazner, pecuniary, posner, pozner