We (the Stan Governing Body) are in the process of working out the details here. We are broadly committed to people being able to use and distribute the Stan software under the relatively unrestricted terms of its licence.
My understanding of what the trademark is for is that while people can use, derive from, distribute, and profit from the Stan software, we don’t want them to be able to say “this is Stan” or in any way imply that something is an intial Stan package if it isn’t.
We are working on some more concrete policies for things like “powered by Stan” logos, but right now if you need something the best way is to email us (board@mc-stan.org). We will do our best to make the process as smooth and straightforward as possible!