As part of your transition from third-party cookies (clientSideMode "required") to first-party cookies (clientSideMode "always"), the "cookieDomain" field may be left blank.
The first party cookies are then deposited directly on the domain of the page consulted. For the site "www.atinternet.com" for example, you will have a cookie domain "atinternet.com" by default. You can also force a fixed value.
Note, in any case, that it is preferable to leave this parameter empty rather than forcing a domain that does not correspond to all the pages, if a level 1 site has pages on several domains, for example. This will prevent the non-deposit of cookies in case of error.