what are the requirements to create a new realm, if that is possible?
As others have said, the only way is to be a duke, and have a duchy that includes a city that is NOT the realm's only city. Then you can secede your entire duchy, thereby creating a new realm. (Note: Your duchy also cannot contain the realm's capital.)
You may find references on the wiki to a Colony Takeover, or CTO. These no longer exist, though may be added back into the game at some time in the future.
to create cities
Again, you cannot change region types. A region is what it is, and will never change. You can build new buildings, and tear down existing buildings, but the region itself won't change.
or other titles like duchies, counties, etc you need to be king,
Kings (rulers in general, not just kings) can create duchies, with certain restrictions. They can also dissolve duchies that don't have any regions in them. Remember that duchies are political organizations, logical groupings of regions. Creating a duchy does not change the map or create regions, or have an really physical manifestation. It simply creates another logical grouping.
the limit is the population right?
Population really only affects how much a region can produce. In some title systems, it also affects the title a lord has. But that's just an RP/flavor thing. It has no real affect on anything.
can you rename a realm if you take over one?
No. Outside of extremely rare, RP-driven events, realm names never change. I can only remember it happening twice in the last 9 years. There is an option to set the "long name" of a realm, but I think it only gets used in one, inconsequential place. The name you give a realm when it is created is essential the name of the realm for as long as it lasts. for some realms, that can be many, many years. For others, it may only be a few days.
