Was the Merrimac a Union ship?

The USS Merrimac had been s ship of the US (Union) Navy. She was in drydock at the Navy base at Norfolk, Virginia when the Rebels were about to capture the Navy Yard, so the withdrawing Union sailors set her on fire, and she burned down to the waterline. The Rebels took what was left of her and built their ironclad on top of the remains, which was the bottom of the ship and its engines. This new vessel looked nothing like the old Merrimac and was renamed the CSS Virginia. So the battle of the ironclads was really the Monitor versus the Virginia. But it sounds so much cooler to be alliterative so the newspaper headlines were "Monitor vs. Merrimac", which had the additional virtue of not recognizing anything the southern government did, such as renaming the remnants of Union ships whose wreckage passed into their hands, on top of which they had built a completely different type of ship.