The word "secede" seems strange here. People say a candidate withdrew or dropped out of the race, if he stopped seeking the nomination.
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They are called running mates when they are running for election.
it is called a presidentceremony
The president appoints someone and the Senate must confirm
In the US government it is called the line of succesion. It starts when the president dies, or quits office.
He is called the "President-elect."