exp show: Preserve full branch and tag names.

Closes #7933

dvc/repo/experiments/show.py

@@ -100,11 +100,10 @@ def _collect_experiment_commit(
                 for refspec in ["refs/tags", "refs/heads"]:
                     name = repo.scm.describe(rev, base=refspec)
                     if name:
+                        name = name.replace(f"{refspec}/", "")
                         break
-            if not name:
-                name = repo.experiments.get_exact_name(rev)
+            name = name or repo.experiments.get_exact_name(rev)
             if name:
-                name = name.rsplit("/")[-1]
                 res["name"] = name
 
     return res
@@ -117,7 +116,7 @@ def _collect_experiment_branch(
     baseline,
     onerror: Optional[Callable] = None,
     running=None,
-    **kwargs
+    **kwargs,
 ):
     from dvc.scm import resolve_rev
 
@@ -132,7 +131,7 @@ def _collect_experiment_branch(
             onerror=onerror,
             status=status,
             running=running,
-            **kwargs
+            **kwargs,
         )
         if len(revs) > 1:
             exp = {"checkpoint_tip": exp_rev}

tests/func/experiments/test_show.py

@@ -48,6 +48,21 @@ def test_show_no_commits(tmp_dir):
     assert Repo.init().experiments.show() == {}
 
 
+@pytest.mark.vscode
+def test_show_branch_and_tag_name(tmp_dir, scm, dvc, exp_stage):
+    with tmp_dir.branch("new/branch", new=True):
+        tmp_dir.scm_gen("branch", "branch", "commit")
+        branch_rev = scm.get_rev()
+
+    result = dvc.experiments.show(all_branches=True)
+    assert result[branch_rev]["baseline"]["data"]["name"] == "new/branch"
+
+    scm.tag("new/tag")
+    tag_rev = scm.get_rev()
+    result = dvc.experiments.show(all_tags=True)
+    assert result[tag_rev]["baseline"]["data"]["name"] == "new/tag"
+
+
 @pytest.mark.vscode
 def test_show_simple(tmp_dir, scm, dvc, exp_stage):
     assert dvc.experiments.show()["workspace"] == {