As an ironclad, the ship was known as the C.S.S. Virginia. Prior to her rebuilding as an ironclad, she had been the U.S.S. Merrimack (named for the Merrimack River). Her name is (and was) often misspelled as "Merrimac" because of a larger, more widely known region of New Hampshire and central Massachusetts that was spelled without the "k". (In fact, Catesby ap Roger Jones was assigned to the USS Merrimack when she was first commissioned to test the first Dahlgren guns that were installed on her. His first three letters to Dahlgren used "Merrimac". After that, he used "Merrimack".)
The misspelling continues today. The fact that the battle at Hampton Roads is often called the battle of "the Merrimack and the Monitor" rather than "the Virginia and the Monitor" may be because much of the press coverage (and hence history) was by Union newspapers and magazines who, along with the Union military, may have knowingly continued to use the prior name of the ship rather than her proper name. Throughout the Official Records, Federal sources referred to the ship as the "Merrimack" while Confederate sources refer to her as the "Virginia." (It appears that the compilers of the Official Records would use the name "Merrimack" regardless of whether the original document had used "Merrimac" or "Merrimack.") Harper's Weekly refers to the ship as "Merrimac". Some Southern sources did refer to the ship as the "Merrimac[k]".
Note that there have been other ships named Merrimac, one during the latter part of the Civil War.
An excellent, but unfortunately obscure, reference on the name is The Mystery of The Merrimack by Edward E. Barthell, Jr. (A copy is at the Hampton Roads Naval Museum in Norfolk.) He traces the early records of the name of the vessel, including some early misspellings of the name. He points out the error in some publications of people who should have known the correct spelling (but, as he also points out, the errors may be by the person who put the document in print). He points out present-day errors at museums (but didn't mention the egregiously misnamed and misspelled Monitor-Merrimac Memorial Bridge Tunnel at Hampton Roads). A number of original handwritten documents (for example, the log of the Monitor for March 9, 1862) show the misspelling. Enclosed is a copy of a letter by Clifford Millard of Norfolk asking for correction on the misspellings of the name on models at two Navy installations and the letter (August 31, 1937) from the Secretary of the Navy directing that they should be corrected.
The Hampton Roads Naval Museum puts out a newsletter called "The Day Book". In Volume 3, Issue 6 (Sept/Oct 1997) "The Museum Sage" feature is entitled "The First Annual Bamboozle Award" on US Navy ship names. The "hands down winner" for Most Confusing went to the Merrimac/Merrimack/Virginia. (Article copied with permission.)