The answer is, to a certain extent yes, and no. Neither the United or Confederate States governments or military issued identification tags to any of its forces in an official capacity. Indeed, while there were various ad hoc methods of identification of the dead that had taken place during the various wars of the 19th century, there were few official issues of identity tags except for possibly an early Prussian experiment in 1866, and official Prussian issues in 1869 and 1870 to combatants. However, it wasn't until after the Geneva Convention in 1906 and its requirements for the victors to protect the bodies of the fallen from abuse, and search the deceased for identifying features or papers that armies began officially issuing them in a widespread fashion (Ashbridge 2020)--1906 is when both Britain and US began issuing official identity tags. Even though John Kennedy, who seems to have been a manufacturer, suggested to Edwin Stanton, the US Secretary of War in 1862 a design for identity tags to be issued to all troops, including illustrated examples. His idea was rejected.

However. The yes side of the answer is the ad hoc side. While there was no official issue, soldiers would take personal agency in trying to insure they didn't become an unknown soldier, lost on the battlefield. They would inscribe or carve names and identifying information on belt buckles, cartridge boxes, and packs. Some elaborately carved mountain laurel roots into tobacco pipe that would bear their name, regiment, corps badge, and battle history (Billings 1887). While clearly not just for identification purposes, they arguably served a dual purpose. Many would write their information on a piece of paper before battle, pinning it to their uniforms, or stuffing it into a pocket.In addition to these personal endeavors, private merchants and sutlers practiced a roaring trade in various types of personal identification artefacts. Period newspapers and periodicals are chocked with advertisements from manufactures, jewelers, and uniform sellers pitching identification pins, discs, watch fobs, etc, all playing on the fear of an unknown, unmourned death.

Sutlers following the armies would mechnically produce cheap brass and lead discs, stamping them with custom identifying information, and mass produced patriotic emblems--eagles, profiles of Washington, slogans about maintaining the Union, etc. Indeed, a pretty stunning example surfaced in the excavations of the Confederate submarine, the H.L. Hunley, belonging to Ezra Chamberlain, Company K of the 7th Connecticut Volunteer Infantry (Neyland 2005). Image here: https://www.hunley.org/wp-content/uploads/2016/09/dogtag-large.jpg). It was likely picked up from Fort Wagner--where Chamberlain died in battle--by the Confederate crewman whose pocket it was found in.

In addition to privately purchased ID tags discussed above, the United States Christian Commission handed out around 40,000 or so paper tags like this one (https://i0.wp.com/gettysburgcompiler.org/wp-content/uploads/2016/10/cwvfm-95_002.jpg?resize=1024%2C627&ssl=1).

If this seems exclusively focused on the Union, that's because there is very little evidence in the form of surviving identity tags, or primary source references, to how Confederate soldiers handled identifying themselves in the event of their death. There are primary references to papers being pinned to uniforms, and personal identifying notes being found post battle in the pockets of dead Confederates, but there is little evidence of the same boom in privately produced material culture specifically focused on identifying the dead, to the best of my knowledge.

Despite these efforts, however, at least half (conservatively) of the total dead from the American Civil War were unidentified.

Ashbridge, Sarah. 2020. “Military Identification: Identity Discs and the Identification of British War Dead, 1914-18.” British Journal for Military History 6 (1): 21–42.

Billings, John Davis. 1887. Hardtack and Coffee. Boston, G. M. Smith & co.

Neyland, R.S., 2005. Underwater Archaeology and the Confederate Submarine H.L. Hunley. Diving For Science 2005: Proceedings of The American Academy Of Underwater Sciences, 61-73.