People who do not register as a member of a political party when running for office are considered?

Libertarian

Democratic

Independent

Republican

People who don't register as a member of a political party when running for office are known as 'independent'

People who do not register as a member of a political party when running for office are considered "Independents". They can choose to do this for many reasons, but usually it's to distinguish a candidate from the party mentality.