Yeah, numerous Communist regimes have/had either "People's" or "Democratic" (or in the case of North Korea, both) in their names. Normally when the Communist regime fell, this was removed,but the main part of the name preserved.
It's not strictly a Soviet thing. When Ukraine declared its independence from Russia back in 1917, it was as "Ukrainian People's Republic", but it was definitely not communist or even particularly socialist. Ditto "Belarusian People's Republic". As I understand, in both cases the intent was to convey that it is a nation-state of the people that inhabit it, and not a part of a large empire anymore.
