No, not usually. Not unless there is some complication or an additional heart condition.
Normally there would not be pain with a heart murmur.
I've had a murmur for decades and never experienced any heart pain.
I will take the other side of the fence and say yes it can. Well, what I'm saying is that you can certainly have chest pain when a murmur exists because it depends on the cause. Most murmurs are harmless but there is always a scale to things. If stenosis of the mitral valve has occurred, giving a murmur, it could be the result of an underlying cause by infection or birth defect, making the heart work much harder than it needs to. This can lead to eventual heart failure. Of course heart disease can also cause the heart to adapt, enlarge, and force the mitral valve out of shape, making a murmur. So while a murmur itself doesn't give the pain, you can obviously have heart problems and pain while a murmur exists.
No one said "it can't". In and of itself, this is highly improbable. Of course you can have pain and a murmur. A murmur in and of itself does not create pain. However thousands of women have murmurs for a lifetime and develop no further problems. Yes. people can have other cardiac related issues that will cause pain, but in terms of making a differential diagnosis, pain is not a defining issue in diagnosing a murmur.
I know. All I was doing was making it clearer in case the poster has a known murmur and now has chest pain. I didn't want the situation where someone would think "I know I have a murmur but this pain can't be my heart because it's highly unlikely to get pain with a murmur". Any pain should be investigated.