Not much in the help on this. How do you...
A. Rename a drum map you've created from the default DMn- name Sonar gives it?
B. Make a drum map you've created globally available to all your Sonar projects?

open the drum map manager and load an existing DM (from the preset drop down).
edit that map as you wish, then save it under a new name, after you save/close the DM, you can then load this map.

OK I guess you're right, you HAVE to select a preset as a starting point if you want to create a new global dm. You can then clear out everything in there and start from scratch. Kinda kludgey but it works.
 
Too bad selecting a preset isn't enforced. I went ahead and created a new map w/o selecting a preset, and now I'm left w/ no way to persist it that I can see.

There are two types of drum map presets. Presets which live in the project and global presets which are available to all projects. The presets saved to disk are the global presets.

It's a problem that the drum map mgr will let you create a drum map w/o starting from a preset from the preset list. Because if you do, there is no way to persist it as a global preset -- and that's pretty much always what you want to do.
 
There is a "blank map" preset in the list, that's handy. 
 
Another really weird artifact of the dm mgr is that when you insert rows, it sets the note value of the next row you insert to the PREVIOUS note value. You have to work DOWN. 
 
And the columns are not sortable. The Help actually says to sort you should move the rows by hand. 
 
 

Yeah, it's a drawback with drum maps going back at LEAST to Sonar 6, probably earlier.
The only way to sort is to drag manually.
 
You can however, go into Sonar's drum map PRV and drag them around in there. It's quicker and easier than trying to do it from the DM Manager