There are getRotation() and getTranslation() methods in class translation, but I’m not sure they can help in my problem. Even so, I still need to know frames of both state vectors.

I’m not sure what you mean here by transition matrix. In Orekit, the state transition matrix refers to the Jacobian of the function mapping initial conditions to final ones.
What are the two position velocity vectors that you’re giving? Are they from two objects at the same time or one at different times?

hello!! I guess i said something incorrectly. These are vectors related to one body at the same time but in different frames. It is easy to calculate the transition matrix between two frames, i just wanted to know if you know one of the frames, is it possible to get the name of the second one, knowing this transition matrix??