Makes sense to me. If you are liars through and through, why be honest on your party's name, of all things?

In Spain it was created by former Francoist hierarchs during the transition from dictatorship to democracy.

I don't see anything unusual about their name.

Any country with "democratic" or "people's" in the name is not democratically run and the people have pretty much no say in anything (Congo, DPRK, etc).

Any armed faction that references a religious figure or text in their name commits atrocities condemned by that religion (LRA, ISIS, etc).

Any state that calls itself "commonwealth" is run by a political elite that does a piss-poor job looking out for the interests of the commoners (maybe worth granting an exception for Kentucky, I've never been there and don't know many people from there so it might be alright).

The car dealership that has radio ads talking about what a great value they are is nothing of the sort.

A political party that prioritizes business over people calling itself the "people's whatever" seems pretty standard as far as naming conventions go.

How the hell did North Korea get the title "Democratic People's Republic"?

Edit: To be clear, I'm not trying to compare the People's Party to the North Korean regime, just pointing out that organisations can pick their own name, and that doesn't necessarily have to reflect what they are, or what they will become years after they have chosen the name.