GPLv3 question regarding server applications

[Bruce C. Miller]

Say you take a project that is a server application, which is released
under the GPLv3, make some modifications to it and then make it
available on the internet for anyone to connect to. This server
doesn't have a client component to it, so, it's similar to a web
application or something like that.

If you were to rebrand your modified version as a new product, would
you still be required under the GPLv3 to make the source available to
the public as well? My reading of the GPL is that, yes, you would have
to, but wanted to check to be sure.