Even if you have no stated policy, it can never be a good idea to give out the name of a patron who has material that someone else is eagerly (and in this case, angrily) awaiting! The likelihood that Prof. A. will harass Prof. B. is simply too great. It might be easier to contact the department that your adjunct works for and ask them to have Prof B. get in touch with you ASAP. (Since both faculty members may belong to the same dept., I doubt it would be wise to even hint to the department representative you're dealing with as to why you need to reach the adjunct prof. Hope that doesn't sound TOO paranoid). Good luck.
Greg