Run currently has a paid add-on ($500) that will hide the Run link from the footer of your web site. This feature can be used for soft white-labeling.

At this time, we do not offer white-labeling of the CMS itself, only the live sites.

Additionally, there are clues hidden in the code of live sites that a sophisticated viewer could use to figure out that your site is hosted on Run, but an average viewer would be very unlikely to.