What is it called when a political party is controlled by a single individual?

When a political party or government is controlled by a single individual that is a Dictatorship, totalitarianism or an autocracy.

Other forms of government rule are:

Democracy: Where the people elect leaders to state and federal positions who will best represent the needs and wills of the those electing them.

Monarchy: Generational leadership based on lineages tied to royalty or blue blood lines.

Oligarchy: A small group of individuals that control government.

Anarchy: Autonomous, individual self government all inclusive to order as well as chaos.

Hope that info helps your quest.