Waldheim's rhymes with:
sondheim's, durkheim's, sondheim's, anytime's, centimes, daytimes, durkheim's, enzymes, halftimes, lifetime's, lifetimes, maritimes, nighttimes, oftentimes, paradigms, pastimes, pulmazyme's, showtime's, sondheim's, wartimes, windchimes
Waldheim's sounds like:
walding, walton's, waltons, welding, weldon's, wielding, wilding, wildness, wilting