Yes, yes, yes, but "rehearse" does not mean memorize and recite. Then it will become a recitation.
Although we say, "Yes, rehearse," you don't want to slice, 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 tell details in ways that reveal the broader story.
You might shape the story for telling with the help of other storytellers. The Guelph Guild members meet regularly from September to June and seek each other's kind input. In addition, many of our members are available for private coaching. Experienced tellers typically continue to appreciate the chance to rehearse before a good coach.
A few other tips: rehearse standing up; rehearse aloud; rehearse in front of 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, realize your tongue can’t get around those words or the audience is confused, there’s a second meaning you hadn’t thought of, 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 the point where they are focused on your anxiety. You don't want to distract from the story.