I can think of four ways to lessen the repetitive use of sentences starting with a nominative pronoun like "She" (other than using the person's name).
Changing the subject to a part or aspect of the character
In some cases, one can present the action as performed by some part or aspect of the person. While this will typically use the genitive form of the pronoun, it can still reduce the perception of repetition. E.g.:
She looked down at her plate and remembered how much she disliked broccoli.
Her eyes dropped down to her plate, even the melted cheese could not cover the recall of her dislike of broccoli.
She was bored. She yawned openly as the lecturer's voice droned on.
Her body ached with boredom, and her uncovered yawn brought no relief as the lecturer's voice droned on.
This kind of change can give an excessive emphasis on the aspect of the character (e.g., the body), potentially reducing the recognition of the character's other attributes. On the other hand, this may encourage an excessive interest in the character because the description tends to seem more vivid; if the reader is meant to identify more deeply with the character, this may be appropriate.
Making the character the object of the sentence
In some cases, one can have an object acting upon the character. This would also not remove the pronoun but change its case (from nominative to objective) and position. E.g.:
She hurried out the shed, fleeing the stench of rotting wood.
The stench of rotting wood chased her from the shed.
She looked at the pearl necklace and longed for a man who thought her worthy of such a gift.
The pearl necklace held her gaze and stirred her longing for a man who thought her worthy of such a gift.
It may not even be necessary to include the character in the action. E.g.:
She returned the plate of uneaten broccoli to the kitchen and went to cure her boredom with some television.
The plate of broccoli returned to the kitchen uneaten; the television's offer of distraction was irresistible.
She slept fitfully and woke unrested to rumpled bed coverings.
The rumpled bed coverings declared another restless night of fitful sleep.
This type of change can give the impression of abstracting the character from the scene. Sometimes this may be desirable for presenting the character as less active (e.g., bored, depressed, or trapped) or perhaps even just to give the scene a more subdued tone or an impression of an uninvolved observer.
Changing an action to a thought
In some cases, the character's action can be translated into a thought. This would typically change the third person pronoun to the first person pronoun. E.g.:
She wondered how long she had been waiting for the bus.
How long have I been waiting for this bus?
She struggled to suppress a bored yawn.
This lecture is so boring. I can barely keep from yawning.
Allowing the reader to read the character's thoughts would work against building a sense of separation or of mystery between the reader and the character or even between the character and others (as if the reader's knowledge leaks to the other characters).
Use filler material
Finally, it is sometimes possible to delay the introduction of the character in the sentence. While this does not remove the nominative pronoun, it reduces the obviousness of its use and the feeling of repetition. E.g.:
She smiled as Sharon came over to her table.
As Sharon approached her table, she smiled.
She pushed fiercely against the stuck door. She knew her stalker was close behind.
The door was jammed; she pushed against it fiercely, knowing her stalker was close behind.
Even interposing a sentence describing the setting can lessen the impression of repetition. E.g.:
She got up and walked alone to the bathroom before leaving.
While a few couples still cuddled in less lit spots, the party was winding down. She got up and walked alone to the bathroom before leaving.
She walked over to the buffet table and started to reload her plate.
The buffet table was fully stocked with comfort foods. She walked over and started to reload her plate.
This kind of change can easily change the pace of the text or distract from the important action. However, it can also be used to provide a richer context for the action.
As noted, these kinds of changes can alter the tone or pace of the text. Even when such a change would work somewhat against the intended tone or pace, it may offer a better tradeoff than repeatedly starting sentences with a nominative pronoun.
It should also be noted that frequent use of nominative pronouns is natural and can be less visible to the reader than one might expect from an abstract analysis. Using the character's name instead of a pronoun can introduce a distance between the reader and the character or emphasize the particular character's action. E.g.:
She pulled apart the drapes. She had never seen the street so peaceful.
Sarah pulled apart the drapes. Sarah had never seen the street so peaceful.
The latter makes the opening of the drapes a stronger, more intentional, more personal action and emphasizes Sarah's perception more and the peacefulness of the street less.