Regarding edit site

Let me set up my question:

I have not seen anything on this, but as one creates new domains in domain mapping it is possible to edit the domain to where it comes up in the admin as instead of this

Now I know that the full domain resolves regardless of whether you edit this area. Is there any need or advantage to edit the domain in these fields? Is there a disadvantage? Does the site look less "more independent" (and less of a network site) to search engines if you get rid of showing the domain as a subdomain of the main site and show it as its own full domain in this backend?

I noted that it does create a login issue at times if you have edited that, requiring a separate login.

I fully understand that just because you can edit something, does not mean that you should edit it.

The reason I ask is that we have done several multisite networks, and wanted to make sure that we do this right.