Is my turtle lonely?

Probably not. Turtles do socialize, and they seek out company when available. This seems to be more than just a survival mechanism. Turtles that live together do interact socially quite a bit. However, a turtle that is kept alone does not stop eating, get sick more often, or behave in ways indicating loneliness.

Since adding a second turtle often creates a lot of problems, and keeping turtles in groups has its own challenges, my recommendation is that if you keep your turtle as a personal pet, that you do not add a companion.