In all literature, not just in Romeo and Juliet or just in William Shakespeare's plays, a character who does not undergo any significant change throughout the story or play is called a static character.
A static character is defined as
"a literary character who undergoes little or no inner change; a character who does not grow or develop."
(Think about the term "static" in science, as well, which means unmoving or unchanging.) Several of the characters in Romeo and Juliet are static characters.
One static character is Benvolio, who is kind and sympathetic throughout the entire play; he is a loyal friend to Romeo and might have been able to avert some of the trouble if Romeo had confided in him. (Obviously Romeo decides not to confide in Benvolio, probably because he knew what his common-sense friend would say and Romeo did not want to hear it.)
Another mostly static character is Paris, who is outraged at the beginning of the play by all the family feuding and of course is equally outraged partway through when he has lost Mercutio, his dead kinsman.
In one way, Romeo is also a static character. Though he changes whom he loves, Romeo is dramatic in his expresssions of love throughout the entire play. In nearly every other way, he is not static.
The opposite of a static character is a dynamic character, and Juliet is the best example of that, as she had no desire to be married one evening and is married by the next evening.