If someone used your credit card without authorization then that is what happened. While I would think that there is a fairly good chance that merely reporting the fraudulent charges shouldn't get you into any additional trouble (and saying you don't recognize the name of the person making the charge, which I'm assuming you don't know), if you want to be safest and feel most comfortable, here are some suggestions:
1. Don't do anything until you speak to a criminal defense attorney.
2. Follow your attorney's advice.
My guess is that you're not only concerned about a charge of solicitation but also of it becoming public knowledge, such as being possibly forced to testify in court (if it ever even came to that.) As such, get an attorney, let him/her manage the matter, and be much wiser then next time you plan to engage in any endeavor.