I am currently in the last interview stages with two companies, A and B. I reached a stage with company A where they are already willing to write me an offer. I have completed three phone interviews with company B (the last one four days ago), and I would like to notify their recruiter that I have a competing offer and hopefully encourage them to "move a bit faster".
How can I politely communicate to the recruiter of company B that, if they are interested in me, they would need to "speed up" the process? Is this a good idea in general? What language could I use for this?
Also, if the recruiter of Company B asks the name of Company A, is it OK if I say I am not comfortable sharing that information? Would that hurt me?