diff --git a/arviz/data/io_cmdstanpy.py b/arviz/data/io_cmdstanpy.py
index 095de475f1..7d74cd1c06 100644
--- a/arviz/data/io_cmdstanpy.py
+++ b/arviz/data/io_cmdstanpy.py
@@ -125,6 +125,13 @@ def posterior_to_xarray(self):
     def sample_stats_to_xarray(self):
         """Extract sample_stats from fit."""
         dtypes = {"divergent__": bool, "n_leapfrog__": np.int64, "treedepth__": np.int64}
+        rename_dict = {
+            "divergent": "diverging",
+            "n_leapfrog": "n_steps",
+            "treedepth": "tree_depth",
+            "stepsize": "step_size",
+            "accept_stat": "acceptance_rate",
+        }
 
         columns = self.posterior.column_names
         valid_cols = [col for col in columns if col.endswith("__")]
@@ -138,7 +145,7 @@ def sample_stats_to_xarray(self):
         for s_param in list(data.keys()):
             s_param_, *_ = s_param.split(".")
             name = re.sub("__$", "", s_param_)
-            name = "diverging" if name == "divergent" else name
+            name = rename_dict.get(name, name)
             data[name] = data.pop(s_param).astype(dtypes.get(s_param, float))
             if data_warmup:
                 data_warmup[name] = data_warmup.pop(s_param).astype(dtypes.get(s_param, float))