How to name a "domain name" without TLD?

Question

Is there a specific name for this kind of "domain name" : https://www.website ?

It's neither a domain name, a hostname, or an URL (because there's no TLD), neither a Second-level domain (because there's https://www.)

Answer 1

There is no specific name because there is nothing specific in your case.

https://www.website is an URL like any other ones, for hostname www.website which is on the TLD website, which is a gTLD, see https://www.iana.org/domains/root/db/website.html

There is nothing special here. You are probably not aware that website is a new TLD.