I work at a large church where we have recently added some new public spaces, including a bookstore and a connection center. Both have their own names: The Source and The Hub. In their designed logos, "the" is shown as lowercase, as you can see in the attached rendering of the spaces.
Several of us are debating whether or not the "t" in "the" should be capitalized when not using the logo, but just referencing the bookstore and connection center in print (for example, in our bulletin: Please sign up for a community group this fall in The Hub.) We've talked about the usage of CamelCase, but weren't sure if it really applies in this instance. We would love your thoughts and feedback.