The fallacy is named because one of the definitions for "beg" is "to evade," which is why "begging the question" can be recast as "evading the question" (although you do lose the subtle part about assuming the conclusion to prove the conclusion).

Thank you. Now I actually learned something from this conversation.

Yes, it's based on a literal translation of a latin idiom: petitio principo (IIRC). A more unambiguous phrasing is: assuming the antecedent.