Hosting own map created by MapTiler Desktop on MapTiler Cloud is very easy.
Create a map with MapTiler Desktop
When creating a map with MapTiler Desktop (or Engine or Cluster), in the step where you are selecting output format, choose MBTiles as an output. This creates a single file, which can be later hosted in MapTiler Cloud.
Upload your map to MapTiler Cloud
After you sign in to MapTiler Cloud, go to Datasets in the left menu and click on New Dataset button. This will lead you to page where you can either drag and drop your map in MBTiles format or browse your computer for the file.
All the functionality is available any time later if you go in administration into Datasets and in My datasets select one of the maps you uploaded previously.
Use your image as part of the map
The image can be used as part of the map itself and rendered altogether with map tiles. This allows you to do things like rendering streets or labels over your image while keeping buildings and landcover under.
To get this functionality, you need to go to Maps, click on one of the maps and select Edit a copy option, which is hidden under three dots just below the map. This will redirect you to the map editor, where you can visually or by writing a code change every possible map element.
Go to Sources in the top right corner and by clicking on any available source you active them. Now click on Add Layer button located in the top left corner, fill in ID based on how do you want the layer with your image to be called, change type to Raster and add Source, which is a name of your source as you add it before (with the + character on the beginning). Your image is on the map!
By drag and drop the layer with your image you can change the order. This means, for instance, move the layer with your image above roads and labels but under landcover and buildings.