The Latin phrase is petitio principii, which literally translates to "request for the principle". Example:
Suppose I believe that taxes are bad for the economy, and I say, "Every time taxes are raised, the economy suffers." I didn't support my belief with a proof, I assumed its truth; I requested that the principle be assumed valid; I begged the question.
"Which begs the question: ..."
This now-ubiquitous phrase is a misuse of the name of the fallacy.
However, we're at a point where it's no problem to continue using it. Everyone knows what's meant by it, and it's fairly natural to use it in conversation. But if you want to use an alternative, you can say:
which prompts the question
which raises the question
which makes one wonder