Well they didn't, but they did.
The common practise was that the race wasn't included in general. But that addendums made in the comments section would indicate the race in some other manner. Comments such as "the slave of so-and-so" and such were often included in these comments sections. However I have also seen muster rolls records which listed the private name as "Big Nose Jim" or "Two Bears". Obviously native american names with no other indications of their nationality. In some cases I have seen Hispanic American names in the muster rolls with no comment and then in the same companys records would appear a Hispanic name with the notation in the comments of "Mexican"? I am assuming that this person was a Mexican National and not an American but fighting on the side of the Confederacy.
But the thing is that none of these identifiers were absolute, nor followed with any type of uniformity.
The southern governmental policy was that the war was a war between "White Men". And for the first two years it was. They did not want the war to become about slavery. To them it was a war of independence and they did not want it to be about anything things else. They were as reluctant to "formerly enlist" blacks for that reason more so than they were worried about "arming" the slaves. But that does not mean that because the Confederate Government was reluntant to formerly enlists blacks that they did not "informerly" serve within the ranks. There were certainly Blacks in the south which the whites trusted with their lives and property. There are numerious accounts of body servant who accompanied their masters into Battle and when the master became injuried or killed they would take his place and continue fighting. Where those men "Formerly enlisted"? I don't think so. Did they fight more than in that one battle? I don't know.
But we do have accounts of a black being the color bearer for a North Carolina Confedrate regiment. Of Hoyt Collier in Mississippi. Of the comments in the 1930's slave narratives of blacks fighting with the Secesh, and of the numbers of free blacks and slaves who served in the hospitals and as cooks and teamsters and built fortifications along rivers and around Richmond and Vicksburg and Atlanta and a hundred other places.
The only place we have a problem with a blacks man service to the Confederate army is did he carry a musket? Well Frederick Douglas, the noted black abolishionist said that they did in Lee's army of Northern Virginia, the strictest of all the Confederate armys in the south so why not more so in the Army of Tennessee, or the Army of the Trans-Mississippi, or even the lesser independent commands such as N.B. Forrest cavalry?
Union reports in the O.R.'s say that they saw blacks on Picket duty standing beside white southern soldiers. They (the Union soldiers making those reports) didn't believe their own eyes because they had been taught not to believe it was possible and we today are still taught to not believe that same thing because it does not fit a popular political concept of why that war was fought.
Like I said I understand where Jim is coming from, about the actual numbers involved, and I can agree with that. But the simple fact that any of the stories of black soldiers and their heroism survived to this day indicates that they were the exceptional cases and that there is much more to this story that has not yet been told. And may never be told.
Of 4,000,000 slaves in the south in 1860 if only 1% helped the southern cause in any way that would have been 40,000 who gave honorable service. It would have only taken 3% of the slaves in the south for the number of blacks aiding the Confederate to equal twice the number of Lee' entire army and the number that served in all the U.S.C.T. regiments. It is statistically impossible to get any group of people as large as the southern slave population to be in total 100% agreement on any matter even their own freedom. The majority of the slaves in the south were treated fairly and not mistreated as is the popular opinion, which support the belief that the 1% figure may well be a low estimation.