Why is the battle of Hampton Roads known as the Monitor vs the Merrimack?

The legal and official name of the Merrimack was the Merrimack. That was the only name it was ever legally given.

The Confederate sates of American was a criminal organization and never had any legal right to do ANYTHING, which includes naming a ship Virginia.

If the Confederacy had won and gained independence and become a legal government, the things it did AFTERWARDS would (mostly) have been legal, but even that would not have made the things the Confederacy did BEFORE gaining independence, such as naming the Merrimack the Virginia, legal.

Therefore it is proper to refer to the ship as the Merrimack, not the Virginia.

The reason why it is so called is that this was the first battle between the armored steamships. For this reason it is famous everywhere in the world not only among historians of the American Civil war.

There is a bit of a theme with American Civil War battles where they tend to have two names; a northern name and a southern one. You will notice that the North liked to name battles after nearby bodies of water, while the South tended to be partial to nearby place names. For example, the Bull Run battles were known in the South as Manassas, and Antietam (named after a nearby creek) was called Sharpsburg in the South.

One other thing you may note from the above discourse is that when there are different names, it is generally the North's name that won out. Probably the simplest explanation for that without going into a lot of gory details is that the North won the war, so they got to write the history books.

That is why I believe the name "Merrimack" tends to be used (note that Wikipedia currently has "Virginia" in parentheses afterwards). From the North's point of view, the Merrimack was a US Navy ship, effectively stolen and modified by rebels.

Merrimack was still in ordinary during the crisis preceding Lincoln's inauguration. Soon after becoming Secretary of the Navy, Gideon Welles took action to prepare the frigate for sea, planning to move her to Philadelphia. The day before the firing on Fort Sumter, Welles directed that "great vigilance be exercised in guarding and protecting" Norfolk Navy Yard and her ships. On the afternoon of 17 April, the day Virginia seceded, Engineer in Chief B. F. Isherwood managed to get the frigate's engines lit off; but the previous night secessionists had sunk light boats in the channel between Cranes Island and Sewell's Point, blocking Merrimack. On the 20 April, before evacuating the Navy Yard, the U.S. Navy burned Merrimack to the waterline and sank her to preclude capture.

So as far as northerners were concerned, the ship was the Merrimack.

As to why it isn't known by a location name ("Battle of Hampton Roads"), that's likely just popular culture for you. The duel between those two specific ships is far more interesting to people than the location it happened to eventually occur at.

It probably doesn't hurt that from the North's perspective the duel ended in a technical win for them (the Confederate ship was the one that retired from the scene). If you look at the entire action, including all ships involved, the Confederates did considerably better.

The Merrimack was renamed the Virginia only after many months of work on the ship. Having called the ship the Merrimack for so long even after it was in Confederate hands, the shipyard workers and crew continued using that name even after the ship's name was officially changed, something I learned at the Monitor Center at the Mariners' Museum in Newport News last year. The Wikipedia page on the Virginia (https://en.wikipedia.org/wiki/CSS_Virginia) says, "After raising, restoration, and outfitting as an ironclad warship [my note: that is, after about 10 months], the Confederacy bestowed on her the name Virginia … the names Virginia and Merrimack were used interchangeably by both sides." My opinion as a writer and editor is that the alliteration of the two names Monitor and Merrimack both starting with an M probably also contributed to people referring to the battle that way.