Parties can be assigned to candidates in the “Candidate setup” screen.
To edit that list of parties, navigate to an election and click the “Parties” button in the upper right.
Click “New party” in the upper right to create a new party.
You can also click the name of an existing party to edit it (which will change the display name wherever it has been assigned to a candidate across this election).
Important: Party names will be used in the context of “Republican Candidate” or “Democratic Candidate for Governor”, so use the form of the word that follows your style in this context (e.g., “Democratic” vs. “Democrat”).