It’s true: there aren’t many other variances from “he,” “his,” and your character’s name. Personally, I use the he/his more than a character’s name, but that can boil down to personal writing style. You definitely want to refer to the character by name when there are multiple people of the same gender mentioned, so we know exactly who “he” refers to.
Amelia stared glumly into the distance for a few moments longer, but no obvious sign answered her prayer. Of course it wouldn’t be that easy. With another sigh, she stood up, brushed off her grass-stained skirt, and began her trek down the hill and back to the village. Marissa had been kind to watch her grandmother for this long, but as nice as the fresh air felt, Amelia didn’t want to abuse her friend’s kindness.
Read your paragraphs out loud. I know that sounds like dorky advice that everyone says, but it might just be you overthinking things. Saying it out loud should help you decide if it’s even a problem at all. In the paragraph above, “her” is used five times. Overused? When I read it aloud, I didn’t think so. The sentence structure and where the “her” is placed is varied enough that the word doesn’t sound overused. Starting a lot of sentences with “he,” “his,” or your character’s name will also make them seem more overused than normal. So, the rest of this answer becomes a thing on mixing up sentence structure so you’re not always starting with “him,” “his,” or your character’s name!
For example, this sounds pretty bad:
She wanted to make sure the room was clean for his arrival. She set the bed first. She wanted to put out fresh flowers as well, but she couldn’t find any. She moved onto the bathroom next, and in minutes it was sparkling clean.
Invert some sentences, add some transitions, and vary your use between the “she,” “her,” and “Amelia,” and we’ve got a paragraph that flows much nicer:
Amelia wanted to make sure the room was clean for his arrival. First, she set the bed. After that she moved on to the bathroom, and in minutes it was sparkling clean. She would have put out flowers as well, but her search for something fresh proved hopeless.
- If you’re going to refer to a character by name, earlier in the paragraph or sentence tends to sound better. This will depend. Again, read it out loud.
- Sometimes you can get away with calling people by other titles, like “the boy” or “the werewolf” or whatever the case may be, but sometimes this can be gimmicky. It will depend on your narrating voice. In any case, this is something to use sparingly. Read it out loud.
- If this is keeping you from getting writing done, calm down. This is generally a line editing focus that you shouldn’t worry about until you’re on one of your draft’s final edits.