Taking credit for supervising a PhD student while I am a postdoc
If you are not yet a professor, you will most likely not yet be the sole one supervising, so there should be a professor who is officially assigned to supervise this student. It might be that you do all the work and the professor is only there on paper, however, he is still the one responsible.
Thus, I would suggest to state in the CV that you assisted professor X in supervising PhD students. Most people will be well aware that this means that you did most of the supervising work, however doing it this way you do not claim something that you (officially) shouldn't be doing.
If you want, ask the professor to write a letter of recommendation emphasizing the fact that you did most of the work.