folder name, e.g.: DEBUG=1 PROFILE_FOLDER=awesomeprofile make
If you are using some aliases to start gaia in Firefox, you will likely need to update these. Here is what I have in my .bash_profile (on OSX) that works well for me:
alias gaiaff="/Applications/FirefoxNightly.app/Contents/MacOS/firefox -profile ~/workspace/gaia/profile-debug"