How should one answer a business phone?

Solution 1:

If your job is such that you would normally be the first person reached when someone calls from outside the company, then you would normally answer by saying something along the lines of your second example (at least giving the name of the company).

If you are not normally the first line of contact, then usually you would answer the phone by giving your particular department (e.g. "human resources") and possibly giving your name, depending on how verbose you want to be.

If you are not normally even the first line of contact within your department, then, depending on your work environment, you could either answer with the department, or just by saying "This is Alex", or "Alex speaking" and possibly adding, "how can I help you?"

Solution 2:

Since all of my calls are direct calls to me I just say:

"Hi/Hello, this is Josh"