I'm not aware of any absolute specific legislation detailing exactly what must be asked for. It's about asking reasonable questions to ensure the identity of the person you are speaking to and can vary from company to company and also on the types of transactions being carried out. That said; name, address and DOB would be the minimum I would expect.
Whilst you may be technically right on this, bottom line is that if your employer wants you to ask four questions, then you ask four. It's probably fair to say that the reason for asking for a telephone number is more to do with ensuring you have correct contact details rather than DPA, but again, if that is what your employer is asking you to do then seems that you are just making life difficult for yourself over this one.
Ultimately, it is their call about the questions they want asked.