Practically speaking, you can live in a socialist environment and 'have your own stuff.' You might want to own a motorcycle and your neighbor might want his car. Technically you both own 'stock' in the factories that make those items.
There are other conceptions of living environments where you live in a commune and have very little personal stuff. But you can do that right here in Amerikay (Get thee to a nunnery).
Also distinguish between democratic societies which are socialist in distribution of wealth, and something like the former Soviet Union where the society was not democratic nor capitalistic, and followed its own philosophy which was so murky you could have two philosophers spouting metaphysical cant at eact other and no one else in the room could tell if they were arguing or agreeing. Communists early distinguished themselves from Socialists and victimized them no end.