In late 80s they ran a TV show with Soviet and American audiences and hosts talking to each other[1]. Once they were a few seconds late to cut off a commercial being shown to the Americans and Soviet public learned that this show had commercials and demanded them to be shown to the Soviet side as well. This should tell you how much advertisement was there.

All I can recall is few absurd billboards like "Fly Aeroflot!" (the only airline) or "Keep your savings in the Sberkassa!" (which probably did not advertise the Sberkassa itself, since it was the only retail bank, but the savings accounts, still looked funny).

1. https://en.m.wikipedia.org/wiki/U.S.–Soviet_Space_Bridge