There's a difference between
changing a word or two, and
omitting a word or two.
The first is NOT OK -- at least in anything to be taken seriously. You might be able to change pronouns, or better, put the referent of the pronoun in brackets.
For example John Doe is talking about another person and it might not be clear from his words alone who he is talking about, so you can add this info in brackets:
John Doe said, "I saw him [my brother] walking in the middle of a busy street."But I don't know what you call this act of putting things in brackets. Is
bracketing a good enough term or you need something fancier?
When you want to omit words or sentences, you use ellipsis marks -- three periods (sometimes four if a sentence break falls within the omitted text) with no space between them.
The rules are quite complex if the words you want to omit are not within one sentence, and the rules also change from one style manual to another. So if you need to be precise, you should check your style guide.