Answer: Army of the Potomac
Ref: Stephen Sears To the Gates of Richmond, page 46. "Johnston himself preferred to continue calling his command the Army of the Potomac as if in deliberate defiance of the Federal Army of the same name."
Edit - In post # 8, Stony provides a link to page 46 of Sears' book, where it says that Johnston reached Richmond on April 12. Sears has a tendency to give dates as month and day only, omitting the year, on the assumption that you have been reading his book page by page and, from following the chronology, you know what year he's talking about.
If you scroll up to the preceding paragraphs and pages, it becomes clear that by the time Sears got to page 46, he was talking about things that took place in 1862. Therefore, Johnston received his orders to take command on April 12, 1862, not April 12, 1861.
Because some players appear to have been confused by the incorrect date stated in the question, I will give credit for Army of the Shenandoah and Provisional Army of the Confederate States as correct answers.
However, I will not give credit for Army of Northern Virginia. While the orders given to Johnston referred to it as the Army of Northern Virginia, Sears' book makes it clear that Johnston's preference was to call it the Army of the Potomac - and the question asked for the name that Johnston preferred.
Hoosier