The name of the Adobe Analytics tracker when using 'Managed by Adobe' in the DTM tool settings is 's'.
I'm guessing that the problem that you are having is that it is not available at global scope.
If you want to expose the 's' object in this scenario, you can do so by adding a line like this in the AA tool (under Customize Page Code). Just open the editor and add a line at the top like this:
window.s = s;
Alternately (but not an officially supported method), you can get a handle to the 's' object from the console by doing this:
var s = _satellite.getToolsByType('sc')[0].getS()
This is a good trick for debugging, but I wouldn't recommend using it in production code.
Cheers,
-Stew