Nomination is the word you are seeking. It comes from the Latin for "naming"
nomination
a person who is running for office is a candidate
A politician who is running for public office is a candidate.
A primary election is a public election run by government officials to determine which candidate will represent a political party in a general election. It is a way for party members or registered voters to choose their party's nominee for a specific office. The winning candidate from the primary election will then go on to compete in the general election.
A person who runs for public office is a candidate, like a presidential candidate.
In some cases, voters can choose a candidate from an apolitical party for public office through a system of open primaries or nonpartisan elections. In open primaries, voters are not required to be registered with a particular political party and can select any candidate, including those from apolitical parties. Nonpartisan elections do not include party affiliations on the ballot, allowing voters to focus on the candidate's qualifications rather than their political affiliation.
In election an individual is chosen for the first time to hold public office; re-election that same individual is chosen to hold public office again.
candidate
A candidate.
Those members of public office who are running for re-election are called incumbents.
If the candidate doesn't have good public opinion, chances are the public won't vote for him or her and they won't get elected.
Often times the term of political manager refers to a person appointed by a candidate running for elective office to advise the candidate on what strategies and tactics are needed to win an election. These managers take public opinion polls on issues relevant to the election campaign and closely watch the results of other polls.
To become a write in candidate for public office a Declaration-of-Write-in-Candidacy must be filed. The declaration must be filed with the Secretary of State of a judge that is local.