The Supreme Court addressed that issue more than fifty years ago in Lyons v. Galanides, Inc., 207 Va. 874, 153 S.E.2d 225 (1967). In Lyons, the appellant's notice of appeal stated that he "hereby gives notice of his appeal from a judgment entered in the above styled case on the 7th day of October, 1965." Unfortunately for Lyons, however, the order entered on October 7, 1965 was not a final order. Under those circumstances, the Court rejected Lyons' argument that he had intended to notice an appeal from the correct order and dismissed his appeal.
Although the Supreme Court has never cited Lyons in a merits disposition, the Court of Appeals did so as recently as 2010. See Evans v. Evans, 2010 Va. App. LEXIS 261 at *10 (Va. Ct. App. June 29, 2010). Moreover, it is possible that the Supreme Court has relied on Lyons in adjudicating motions to dismiss. Because the Court does not usually publish those orders, it is hard to say. Thus, the only safe assumption is that Lyons remains good law.
So what is an attorney to do? Although Rule 5:9 does not require that a notice of appeal specify the date of the final judgment, everyone seems to do it. And there are good reasons for that, especially where trial courts require it.
Unfortunately, I think the answer is rather unsatisfying: Make absolutely certain that your notice of appeal correctly identifies the final order, or risk dismissal.