As a child, all the texts book speak of that first iron-clad battle as between the Monitor and Merrimack, not Virginia. Gosh- THOSE books were ancient even then and must have been written a lot of years closer to the end of the war than you'd think. I only untangled that recently, in point of fact, thought it was the other way around.
The name "Merrimack" has stuck for a number of reasons... One may simply be the alliteration of
Monitor and
Merrimack. Another is that a lot of the naval history has an inherent Northern bias, because the Union Navy was so much larger than the Confederate Navy, and because most (fortunately not all) of the Confederate naval records were lost at Richmond at the end of the war.
But an important third reason was that the name
Virginia was not too widely known or used at the time. I'm not precisely sure when the name was first applied to the converted ironclad, but Southern sources consistently refer to the vessel as "Merrimac" throughout her conversion process, and John Mercer Brooke, one of her designers, often continued to refer to her as "Merrimac" even after she was technically the
Virginia.
Virginia is clearly most correct when referring to the operational Confederate ironclad, but the use of
Merrimack and
Merrimac are entirely understandable due to these various considerations. John V. Quarstein, in his books about Hampton Roads, calls her the
Virginia when writing from a Southern point of view, the
Merrimack when from a Union point of view, and uses whatever the people used at the time (often
Merrimac) when quoting the originals directly.
My rule is to call her the
Virginia whenever she's mentioned as actively operating under the Confederate flag, and to use "CSS
Virginia (ex-USS
Merrimack)" if I feel there's a possibility of confusion.