What is the name of a long speech made by a character that other characters hear called?
a. an aside
b. a dialogue
c. a monologue
d. a soliloquy

The answer is letter c.   A monologue is a kind of speech which is delivered by one person . It is a long one-sided conversation.  On this dramatic device, only one person does the talking.  

An aside is a device used in drama wherein a character speaks to the audience and the audience, in convention, is to realize that the speech of the character is unheard by the other characters on stage.
A dialogue on the other hand is a spoken or written exchange of conversation between two or more people.
Soliloquy comes from the Latin words “solo” and “loquor”  which means “to oneself “ and “ I talk”, respectively. It is a device commonly used in drama whereby the character speaks to himself or herself, conveying thoughts and feelings, thereby sharing them with the audience.