Such a move for "change of scenery" would be usually dissuaded, especially that if you consider that Communist countries' policy assumed full employment - if you didn't have a work place ready, you'd be assigned one, preferably in your profession and in your general region. To obtain insurance and social services, you had to register in your new adress, but this was less common in rural regions. The Soviet Union proper used "internal passports" - another form of ID you needed to board a train or rent a bed in a hotel. A large portion of workers, on the other hand, were migrants, and followed the "new and developing" factories, to Kazakhstan or Siberia, since it paid better.

Of course, there were exceptions, but most of time they either involved major projects and official invitation (diplomats, scientists, engineers, university students) or assuming another citizenship (mostly thanks to marriage). The Baltic republics, in particular Latvia and Estonia, today still struggle with Russian majority that was imported after WWII.

In general, authoritarian systems aren't happy when people aren't in their place.