One of the bits of advice given to fledgling writers in the current era is “the spellchecker is your friend.”
Like a lot of advice-for-writers, this advice is both true and not-true. Or, to put it another way, the spellchecker is your friend, but it’s not your best friend. It’s the friend who’s fun to be with and helpful on the easy stuff, but who’s nowhere in sight when you’ve got a lot of heavy lifting to do, or the one who’s got your back right up to the point where they run off with your prom date.
A spellchecker will catch your typos, and it will catch your misspellings . . . but only so long as the typos and misspellings aren’t also legitimate words in your spellchecker’s language-of-choice. It won’t do you a bit of good with the its/it’s problem, or the to/two/too problem, or the there/their/they’re problem, or any of those fatally similar and easily confused homonyms. It won’t remind you to put apostrophes in your possessives, and it won’t catch embarrassing stuff like pubic for public or untied for united.
As for your characters’ names, or for any terminology coined especially for the story you’re working on . . . unless you remember to add those words to the spellchecker’s user dictionary, it’s not going to keep you from messing those up either. And heaven help you if you accidentally add a wrong spelling to the user dictionary, because getting in there and taking it out again is not something most word processors tend to make easy.
The sad fact is that spellchecker or no spellchecker, there’s still no substitute for going over your manuscript by hand and eye before sending it out.