Yes. Radio Moscow used to broadcast all over the world. You can listen to an audio clip of their American broadcast here. (The propaganda starts at 00:30 with "fan mail" from an enthusiastic listener.) The other Warsaw Pact countries also had their own shortwave broadcasts, including Radio Romania International and Radio Polonia. Some of them are still active, although they tend to be dropping shortwave in favor of the internet. And they don't air communist propaganda anymore. (With the exception of Voice of Korea.)

It was called Radio Moscow during the Cold War years. After the end of the Soviet Union it was rebranded the Voice of Russia. See some boiler plate about their history here.

Now it's being merged together with other Russian government run news outsets into a larger Rossiya Segodnya organization. I guess there is some question as to whether it will include the RT Television network or not. But it seems likely that they will at least complement once another when it's done.