Mattermost source code is available under an open source license and you are not restricted from changing the Mattermost name and logos to something completely different and compiling your own version.
Enterprise Edition offers convenience features for adding custom branding. The wording in Enterprise Edition is now changed to "Tools for custom branding" instead of "Whitelabeling", to be more clear. There is no option in Enterprise Edition to entirely remove Mattermost branding.
Mattermost switched releases to an MIT license in 2015 and you can read the announcement on the reasoning behind the change.