Jurisdiction and conflicts belong in the first three questions
Two minutes of screening decides whether the next thirty are worth anyone's time.
Whoever answers the phone should be asking, in the first minute, where the caller lives, where the other party lives, and how long each has been there. Not because the answer is dispositive, it often is not, but because it determines who at the firm should be on the call and whether the matter belongs to you at all.
Both parties' names come next, for the conflict check. A conflict check that takes two days is a case handed to whoever answered faster, and in a metro with this many firms someone always answers faster.
Write the script down and put it in front of whoever is on the phone. Intake in most small firms is done by whoever is nearest, which means the quality of the first two minutes varies by who picked up. A one page script removes most of that variance.
Log the answers in a structured field, not in a note. Jurisdiction, matter type and source have to be data if you ever want to see which of your three markets is actually producing work.