When we’re talking about the domains or custom domains, we’re specifically talking about the domain and TLD part of a web address as shown here:
On the Starter plan, you get to choose the subdomain, which is used as part of the discourse.group domain. So your-custom-name.discourse.group ends up being your Discourse site’s web address.
When you upgrade to higher plans like Pro, you can optionally customize both the subdomain and the second-level domain by using a domain you’ve leased from a registrar like namecheap.com or porkbun.com.
That’s when you’d need to follow instructions in Configure your domain name for hosted Discourse to get a fully custom web address like forum.example.com or myawesomeforum.com instead of example.discourse.group
The path section of the address generally can not be changed.
Can you be more specific about where you see these? are you looking to change the text on your site in specific places? (screenshots may help)