It's a common propaganda tactic to use simple names to associate ideas or feelings with the thing you want to promote.
In Soviet Russia the state propaganda press was called Truth. Orwell makes great note of all these things.
Calling it the peoples vote is meant to support their agitprop tactic of pretending that the first vote was a sham, orchestrated by "them", and based on disinformation.
It's rather amusing, considering that before the referendum, Remainers would rubbish the idea of a forced second vote (as happened in Ireland, Holland etc) as conspiracy theory and here they are (the EU and neolibs) attempting to do just that. It's laughable.
If there is a second vote, the public has no reason to vote ever again.