diff --git a/.pre-commit-hooks.yaml b/.pre-commit-hooks.yaml
index bf58b4b97..d81f3da64 100644
--- a/.pre-commit-hooks.yaml
+++ b/.pre-commit-hooks.yaml
@@ -8,7 +8,7 @@
   name: DVC pre-commit
   require_serial: true
   stages:
-  - commit
+  - pre-commit
   verbose: true
 - args:
   - git-hook
@@ -20,7 +20,7 @@
   name: DVC pre-push
   require_serial: true
   stages:
-  - push
+  - pre-push
 - always_run: true
   args:
   - git-hook
@@ -29,7 +29,7 @@
   id: dvc-post-checkout
   language: python
   language_version: python3
-  minimum_pre_commit_version: 2.2.0
+  minimum_pre_commit_version: 3.2.0
   name: DVC post-checkout
   require_serial: true
   stages:
diff --git a/dvc/repo/install.py b/dvc/repo/install.py
index 149e1ae95..ddf274d3a 100644
--- a/dvc/repo/install.py
+++ b/dvc/repo/install.py
@@ -1,5 +1,6 @@
 from typing import TYPE_CHECKING
 
+from dvc import version_tuple
 from dvc.exceptions import DvcException
 
 if TYPE_CHECKING:
@@ -16,19 +17,19 @@ def pre_commit_install(scm: "Git") -> None:
     with modify_yaml(config_path) as config:
         entry = {
             "repo": "https://github.com/iterative/dvc",
-            "rev": "main",
+            "rev": ".".join(map(str, version_tuple[:3])),
             "hooks": [
                 {
                     "id": "dvc-pre-commit",
                     "additional_dependencies": [".[all]"],
                     "language_version": "python3",
-                    "stages": ["commit"],
+                    "stages": ["pre-commit"],
                 },
                 {
                     "id": "dvc-pre-push",
                     "additional_dependencies": [".[all]"],
                     "language_version": "python3",
-                    "stages": ["push"],
+                    "stages": ["pre-push"],
                 },
                 {
                     "id": "dvc-post-checkout",