I would expect a short text introduction clarifying that I am about to add a new domain name for an existing site, as opposed to registering a new site.
There is no message, explanation or links to the documentation letting the user what they are about to do and offering a link to the "Register a new site" flow should they be looking for that other option (as it is often the case.
I find this a lot in chat and tickets. A user intends to register a new (different) site buy will instead add a secondary domain to their current page, which can be rather confusing. A simple text with a couple of links will reduce frustration, confusion and support time.
MacOS 10.13.6 (17G2307)
Google Chrome 79.0.3945.88
I made this mockup.

The text could go along these lines:
Here is the corrected version of the text we could use (or something to that effect)
You are about to register a new domain for CurrentPrimaryDomain. This domain will be added to your site SiteAddress. This is not the same as creating a new site. If you want to create a separate new site please click here.
You can click here to learn more about domains.
This is a rather common recurring issue:
h16476864-hc 16478017-hc 16479872-hc
Also, discussed here: p9ag8j-Vh-p2
@fditrapani, IIRC, something like this was already on your radar as part of the domain management revamp?
@klimeryk I'll be working on moving domains between sites which tackles this from another angle but this brings up a good point which I think might be worth trying. I am hesitant to add a lot of copy to the screen since you have a PR to update this screen to show results right away. I wonder if we could simplify this by just starting with the title and then layering on more if we don't see it improving? Something like this if Filippo Di Trapani is the site title:

A user intends to register a new (different) site buy will instead add a secondary domain to their current page
Just noting there's an issue for that in #27932, where no solution is available currently. My understanding is that the idea is not to change this page specifically, but rather improve clarity of creating a new site in general.
Thanks @Aurorum! I'll close this issue in favour of that one because it looks like you all are having some extensive conversations around it.