Is it permissible to use programs with names and logos that carry certain religious connotations, such as "Canonical" and Ubuntu's Trinity symbol, or "Enlightenment," or "Trinity"? And is the prohibition of using them similar to pirating alternative software?

The mere fact that a program's name or logo carries an incorrect implication does not preclude its use, unless it leads to the promotion of falsehood, in which case it is prohibited as a deterrent (sadd al-dhari'a). Using something that bears forbidden logos in a way that involves promoting them is considered cooperation in sin, which is forbidden. As for pirating software, it is an infringement on the rights of its owners, but if promoting falsehood and spreading disbelief result from using such programs, their harm is greater than infringing on copyright.