(New York, NY)
Hi. Was wondering if the dialogue should always end with she responded or he asks, etc.? Can it be written in script format with the character's name first and then his/her dialogue or are both ok within the same story? For example..
"I'm not talking to you" Claire yelled.
Claire-"I'M NOT TALKING TO YOU!!!
You don't need a speech tag (e.g. "Clair said") with every line. In a two person dialogue, most tags can be left out once the speaking order is established. However, a few tags now and then in long passages of dialogue can help the reader keep track of who is speaking.
An alternative to tags is to use action beats. If you have a character perform an action followed by a line of dialogue in the same paragraph, the reader knows the character who did the action also spoke the line. Sometimes a character's thoughts or feelings can serve the same purpose (e.g. "I felt my face flush").
The nice thing about beats is that they reinforce the reality of the scene. It can also be more efficient to have characters carry on a conversation while they do something rather than talk and act at different times.
However, as with speech tags, you shouldn't use action beats with every line. The general rule is that you don't want tags or beats to distract too much from the dialogue, unless for example a particular action is important to the story. So use both sparingly, just enough to help the reader be clear about who says what.
Under no circumstances should you use playscript format in a novel. For that matter, don't use all caps or more than one exclamation point. If it isn't obvious from the words that the character is angry or distraught, rewrite the line or use a stronger verb (as in your example of "Claire yelled").
Most of the time "said" is the best verb to use in speech tags because it doesn't draw attention to itself, putting the focus on the dialogue itself which is where the characterization usually is found.