Yes, yes, yes, but "rehearse" does not mean memorize and recite and recite. Then it will become a recitation.
Although we say, "Yes, rehearse," you don't want to slice and dice and overthink a story. That may sound contradictory but you want to know and feel the flow of the story and then live it and be open to spontaneity in response to the story and the audience.
Add emotions and telling details in ways that reveals the broader story.
You might shape the story for telling with the help of other storytellers. Many of our members are available for private coaching. Experienced tellers typically may continue to appreciate the chance to rehearse in front of a good coach.
A few other tips: rehearse standing up; rehearse aloud; rehearse in front ot a full length mirror; pay attention to your hands, your posture, your face, your tone, your pacing, . . . Experiment to develop your talents. Have fun!
Plan for a beginning to introduce your story in a way that informs and grabs your listeners, know the FLOW of the middle to unfold the story, and plan a closing that lets your audience know it is the end.
Rehearse recovery. Don't backtrack.
The first telling to an audience may be rough. You may forget things, or realize your tongue can’t get around those words, or the audience is confused, or there’s a second meaning you hadn’t thought of, or there's an unplanned interruption, or any of a dozen other things. Part of rehearsing is planning for those moments and rehearsing a smooth recovery, unbeknownst to your audience as much as possible.
Do NOT let your listeners know of your discomfort to a point where they are focussed on your anxiety. You don't want to distract from the story.