Question: 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?

Answer: 
I have noticed that the moment you mention something about competing offers, the focus of the recruiter shifts to the details of the offers that you may have.
They try to coerce you to tell them about it stating that they would match it.
That might not be what you intended and it becomes a bit uneasy at times.
If this is a third party recruiter then yes. That recruiter is working for you. So letting the recruiter know he needs to get an answer can help. If the company needs more time they will tell the recruiter that. And the recruiter will navigate the protocols for you.

Otherwise, it depends on what your reason for pushing is. If you just want to compare offers then pushing them will probably not hurt. After all if the company decides not to make an offer then the result is the same as if you just took the offer from company A. 

If you are wanting to work for Company B and Company A is willing to sit on the offer I would give company B as much time as you can. I would continue to probe company B to see what the status is once a week to make sure that you are still being considered. 

When you are ready to commit to A then, I would contact the recruiter at company B and let him know that you have a company that intends to extend you an offer in the next few days. You are interested in working with company B but unless you have an offer from them to consider you will be accepting the offer. Worst case Company B wishes you well in your career with Company A.