Depends on whether or not his body could be identified by friends. Normally Federal burial details had no reason or ability to do so. They would dig shallow trenches and fill them with Confederate dead.

In the case of Confederate dead from the Chickamauga battlefield, bodies were removed to Marietta GA for burial. Here's an interesting link to that cemetery (one of many) that gives examples of identified and partially identified burials --
http://www.mindspring.com/~sixcatpack/confed.htm