Translation:Do you know that woman's name?
The verb here is the progressive form of 知る (meaning "to know"), for anyone wondering.
I think I finally understand why I hear Japanese English learners say things like "do you knowing her?" It's the same reason that I, as an English speaker, want to say "彼女を知りますか?"
On mobile, after I picked out the correct sentence, all that was left was "in bed". I suppose that's an important time to know her name.
How will the meaning of this sentence change if we replace particle 'wo' with particle 'ha'?
It would then mean "does that woman's name know?" which of course doesn't make sense.
You're talking about a specific woman here, the subject of the sentence. I hope someone will correct me if I'm wrong, but I think you just wouldn't use 'ha'.
I'd very much like confirmation/correction on this, but my gut feeling is that 名前を ends up with emphasis on the verb, while 名前は ends up with emphasis on the name.
"Do you KNOW that woman's name?" vs "Do you know that woman's NAME?"
Please correct me.
It would translate to "do you know her name?" The only difference is that it would probably sound weird to Japanese speakers because that's not the tense they would use.
I think that it is generally assumed that the speaker is asking the question to someone other than self.