diff --git a/newsfragments/1165-PROJECT_NAME-interpolation.bugfix b/newsfragments/1165-PROJECT_NAME-interpolation.bugfix
new file mode 100644
index 00000000..e4200e0a
--- /dev/null
+++ b/newsfragments/1165-PROJECT_NAME-interpolation.bugfix
@@ -0,0 +1 @@
+- Fixed interpolation of the environment variable **COMPOSE_PROJECT_NAME** when it is set from the top-level **name** value within the Compose file.
diff --git a/newsfragments/1165-project-name-evaluation-order.bugfix b/newsfragments/1165-project-name-evaluation-order.bugfix
new file mode 100644
index 00000000..d8834e17
--- /dev/null
+++ b/newsfragments/1165-project-name-evaluation-order.bugfix
@@ -0,0 +1 @@
+- Fixed project name evaluation order to match the order defined in the [compose spec](https://docs.docker.com/compose/how-tos/project-name/#set-a-project-name).
diff --git a/podman_compose.py b/podman_compose.py
index df1f9ee9..62ec408e 100755
--- a/podman_compose.py
+++ b/podman_compose.py
@@ -1980,6 +1980,25 @@ def _parse_compose_file(self):
                 sys.exit(1)
             content = normalize(content)
             # log(filename, json.dumps(content, indent = 2))
+
+            # See also https://docs.docker.com/compose/how-tos/project-name/#set-a-project-name
+            # **project_name** is initialized to the argument of the `-p` command line flag.
+            if not project_name:
+                project_name = self.environ.get("COMPOSE_PROJECT_NAME")
+                if not project_name:
+                    project_name = content.get("name")
+                if not project_name:
+                    project_name = dir_basename.lower()
+                # More strict then actually needed for simplicity:
+                # podman requires [a-zA-Z0-9][a-zA-Z0-9_.-]*
+                project_name_normalized = norm_re.sub("", project_name)
+                if not project_name_normalized:
+                    raise RuntimeError(f"Project name [{project_name}] normalized to empty")
+                project_name = project_name_normalized
+
+            self.project_name = project_name
+            self.environ.update({"COMPOSE_PROJECT_NAME": self.project_name})
+
             content = rec_subs(content, self.environ)
             if isinstance(services := content.get('services'), dict):
                 for service in services.values():
@@ -2012,19 +2031,6 @@ def _parse_compose_file(self):
             log.debug(" ** merged:\n%s", json.dumps(compose, indent=2))
         # ver = compose.get('version')
 
-        if not project_name:
-            project_name = compose.get("name")
-            if project_name is None:
-                # More strict then actually needed for simplicity:
-                # podman requires [a-zA-Z0-9][a-zA-Z0-9_.-]*
-                project_name = self.environ.get("COMPOSE_PROJECT_NAME", dir_basename.lower())
-                project_name = norm_re.sub("", project_name)
-                if not project_name:
-                    raise RuntimeError(f"Project name [{dir_basename}] normalized to empty")
-
-        self.project_name = project_name
-        self.environ.update({"COMPOSE_PROJECT_NAME": self.project_name})
-
         services = compose.get("services")
         if services is None:
             services = {}
diff --git a/tests/integration/env-tests/container-compose.yml b/tests/integration/env-tests/container-compose.yml
index 3a8b28eb..4498f09d 100644
--- a/tests/integration/env-tests/container-compose.yml
+++ b/tests/integration/env-tests/container-compose.yml
@@ -1,5 +1,7 @@
 version: "3"
 
+name: my-project-name
+
 services:
   env-test:
     image: busybox
@@ -8,3 +10,9 @@ services:
       ZZVAR1: myval1
       ZZVAR2: 2-$ZZVAR1
       ZZVAR3: 3-$ZZVAR2
+
+  project-name-test:
+    image: busybox
+    command: sh -c "echo $$PNAME"
+    environment:
+      PNAME: ${COMPOSE_PROJECT_NAME}
diff --git a/tests/integration/env-tests/test_podman_compose_env.py b/tests/integration/env-tests/test_podman_compose_env.py
index 351644f3..f1c35cf4 100644
--- a/tests/integration/env-tests/test_podman_compose_env.py
+++ b/tests/integration/env-tests/test_podman_compose_env.py
@@ -36,3 +36,54 @@ def test_env(self):
                 compose_yaml_path(),
                 "down",
             ])
+
+    """
+    Tests interpolation of COMPOSE_PROJECT_NAME in the podman-compose config,
+    which is different from external environment variables because COMPOSE_PROJECT_NAME
+    is a predefined environment variable generated from the `name` value in the top-level
+    of the compose.yaml.
+
+    See also
+    - https://docs.docker.com/reference/compose-file/interpolation/
+    - https://docs.docker.com/reference/compose-file/version-and-name/#name-top-level-element
+    - https://docs.docker.com/compose/how-tos/environment-variables/envvars/
+    - https://github.com/compose-spec/compose-spec/blob/main/04-version-and-name.md
+    """
+
+    def test_project_name(self):
+        try:
+            output, _ = self.run_subprocess_assert_returncode([
+                podman_compose_path(),
+                "-f",
+                compose_yaml_path(),
+                "run",
+                "project-name-test",
+            ])
+            self.assertIn("my-project-name", str(output))
+        finally:
+            self.run_subprocess_assert_returncode([
+                podman_compose_path(),
+                "-f",
+                compose_yaml_path(),
+                "down",
+            ])
+
+    def test_project_name_override(self):
+        try:
+            output, _ = self.run_subprocess_assert_returncode([
+                podman_compose_path(),
+                "-f",
+                compose_yaml_path(),
+                "run",
+                "-e",
+                "COMPOSE_PROJECT_NAME=project-name-override",
+                "project-name-test",
+            ])
+            self.assertIn("project-name-override", str(output))
+        finally:
+            self.run_subprocess_assert_returncode([
+                podman_compose_path(),
+                "-f",
+                compose_yaml_path(),
+                "down",
+            ])