Minecraft map?

For example, can you mark your house and name it, and if so, how

There's a mod called Xaeros Minimap. You can mark and name places and even have a map displayed the whole time.

Is it also possible without mods?

As far as I know, no. You can only write down the coordinates and remember where what is

You can rename and place banners in the anvil. After that you have to right click on the banner with a card.