diff --git a/CHANGELOG.md b/CHANGELOG.md
index fe691a95a9..77d5d54c56 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -14,6 +14,7 @@
 * Integrate `index_origin` with all the library ([1201](https://github.com/arviz-devs/arviz/pull/1201))
 * Fix pareto k threshold typo in reloo function ([1580](https://github.com/arviz-devs/arviz/pull/1580))
 * Preserve shape from Stan code in `from_cmdstanpy` ([1579](https://github.com/arviz-devs/arviz/pull/1579))
+* Updated `from_pystan` converters to follow schema convention ([1585](https://github.com/arviz-devs/arviz/pull/1585)
 * Used generator instead of list wherever possible ([1588](https://github.com/arviz-devs/arviz/pull/1588))
 * Correctly use chain index when constructing PyMC3 `DefaultTrace` in `from_pymc3` ([1590](https://github.com/arviz-devs/arviz/pull/1590))
 
diff --git a/arviz/data/io_pystan.py b/arviz/data/io_pystan.py
index 8690e9aa32..90ce5321bc 100644
--- a/arviz/data/io_pystan.py
+++ b/arviz/data/io_pystan.py
@@ -627,6 +627,14 @@ def get_sample_stats(fit, warmup=False):
     """Extract sample stats from PyStan 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",
+    }
+
     ndraws_warmup = fit.sim["warmup2"]
     if max(ndraws_warmup) == 0:
         warmup = False
@@ -653,17 +661,16 @@ def get_sample_stats(fit, warmup=False):
         dtype = dtypes.get(key)
         values = values.astype(dtype)
         name = re.sub("__$", "", key)
-        name = "diverging" if name == "divergent" else name
+        name = rename_dict.get(name, name)
         data[name] = values
 
     data_warmup = OrderedDict()
     if warmup:
         for key, values in extraction_warmup.items():
             values = np.stack(values, axis=0)
-            dtype = dtypes.get(key)
-            values = values.astype(dtype)
+            values = values.astype(dtypes.get(key))
             name = re.sub("__$", "", key)
-            name = "diverging" if name == "divergent" else name
+            name = rename_dict.get(name, name)
             data_warmup[name] = values
 
     return data, data_warmup
@@ -773,6 +780,14 @@ def get_sample_stats_stan3(fit, variables=None, ignore=None):
     """Extract sample stats from PyStan3 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",
+    }
+
     if isinstance(variables, str):
         variables = [variables]
     if isinstance(ignore, str):
@@ -789,7 +804,7 @@ def get_sample_stats_stan3(fit, variables=None, ignore=None):
         dtype = dtypes.get(key)
         values = values.astype(dtype)
         name = re.sub("__$", "", key)
-        name = "diverging" if name == "divergent" else name
+        name = rename_dict.get(name, name)
         data[name] = values
 
     return data