The type of conflict in which a character struggles with himself and has trouble deciding what to do is called

self vs. self or man vs. self

http://www.storyboardthat.com/articles/education/types-of-literary-conflict

It's also sometimes called "internal conflict".

The type of conflict you are referring to is called internal conflict. Internal conflict occurs within a character's mind and involves their struggles, doubts, and emotional turmoil. This type of conflict usually involves the character having to make a difficult decision or facing a moral dilemma. In order to identify the type of conflict in a story, a reader can analyze the character's thoughts, emotions, and inner dialogue, as well as their actions and choices throughout the narrative.