In casual speech many people use the expression "to beg the question" to mean "to raise another question". However, "beg the question" is a phrase from formal logic that was created in the 16th century as a translation for a concept that Aristotle wrote about, "petitio principii", which could be better translated as "assume the question. A statement "begs the question" when it is a circular argument. For example, "Reasonable people are those who think and reason intelligently." This statement begs the question. What does it mean to think and reason intelligently? So, when you see this expression, you have to consider whether they are saying that answering one question leads to another question (that is "raises the question"), or whether they are saying that some other statement is a circular argument (that is, something is what it is because it is what it is).

Languages change. Nowadays, the supposedly “wrong” usage is well established, and far more common than the supposedly correct one, even among educated native speakers. It’s up to you how you want to use it, but it's the twenty-first century, and I’m with Merriam Webster: https://www.merriam-webster.com/words-at-play/beg-the-question

You can use raise or beg, it means the same thing.