Learn Swedish: Vad kallar man det här?

In English, we often use "you" to mean "people in general". In Swedish, you use the pronoun man (which means "one") for this general meaning. If you asked Vad kallar du det här?, you would be asking what the specific person you are talking to calls it, rather than what its actual name is.

Why is it det här and not den här?

Both mean "this", but Swedish defaults to the neuter form (det) when you are pointing to an unknown object. Since you are asking what the thing is, you do not know if it is an en word or an ett word yet, so you must use the default det här.

Could I use the verb heter instead of kallar man?

Yes! Vad heter det här? (What is the name of this?) is a very natural alternative. Vad kallar man det här? is just another common way to ask the same thing, focusing slightly more on what people generally call the object.

Does the verb kallar work exactly like "call" in English?

It works for calling something by a name or title. However, if you mean "call" as in making a phone call, you must use ringa. If you mean "call" as in shouting out to someone, you use ropa.