Proper way to change domain name

Yes, that is what the two fields are for. If, contrary to expectations, something goes wrong, check what is written under the article: https://wordpress.org/support/article/changing-the-site-url/

Remember beforehand:
* Make sure that the new domain already points to your hosting.
* Make a backup of your project.

Your hoster could help you with both.

I’ve read a lot of posts where people have done this and it turns into a disaster.

After years of dealing with such issues, I can definitely say that most of these “disasters” are self-inflicted. I’ve dealt with numerous cases here and elsewhere where:

• People use unregistered domains (yes, this happens — and not just typo!)
• People make mistakes typing their registered domain names
• People do not point their domain (registered elsewhere) to their hosting account (or the right website folder in their hosting account)
• Some do not have SSL certificate setup but read somewhere that HTTPS is good for SEO and they just jump in and change their addresses to use HTTPS

And even when all the prep work has been done correctly, a common occurrence is people just changing the two address fields, but not doing a search-and-replace on their database to swap all occurrences of the old domain with the new one. The end result is broken images and files.