In 2021, there were attempts by the federal People's Party of Canada (PPC) to register the name "People's Party of Ontario" with Elections Ontario. The elections agency rejected the name five times due to its similarity to the existing Peoples Political Party.

Wiki about PPC Name Dispute

It looks like the PPC vs People's Political Party (now defunct) was over naming rights only with Elections Ontario for running in Ontario provincial elections for the Queen's Park legislature in Toronto, not the federal one in Ottawa.

It seems at one time the PPC tried to register a sister Ontario provincial wings for the provincial legislature, much like the Conservatives, Liberals and NDP each have a provincial party in the Ontario legislature.

I do somewhat recall after COVID and the convoy that there were rumblings that former Doug Ford PC MPP Randy Hillier was going to try to form a PPC Ontario wing and lead it against his old party in June 2022.

But Hillier is kind of an oddball and a loose cannon, so he announced well before the writ dropped that spring that the PPC Ontario project wasn't happening.

The PPC naming dispute in Ontario re: their state legislature has no effect on the federal PPC or this current election though.