docs(image): document Docker image naming mismatch

Add OCI title/description labels to the Dockerfile, note the
docker.gitea.com/gitea-mcp-server vs gitea-mcp naming mismatch in each
README with a link to a new docs/adr note recording the maintainers'
preferred gitea/mcp-server direction from issue #181, and add a test
that keeps the README image references consistent.

Co-Authored-By: Codet <codet@commitgo.dev> (GPT-5-Codex)

operation/readme_test.go

@@ -22,6 +22,38 @@ var readmeAccessLabels = map[string]map[string]string{
 	"../README.zh-tw.md": {"讀取": "read", "寫入": "write"},
 }
 
+// publishedDockerImage is the image name published for this project. See
+// docs/adr/docker-image-naming.md for why it differs from the repository name.
+const publishedDockerImage = "docker.gitea.com/gitea-mcp-server"
+
+// dockerImageReference matches any docker.gitea.com/<name> image reference so
+// stray typos or partial renames in the README files can be caught.
+var dockerImageReference = regexp.MustCompile(`docker\.gitea\.com/[a-zA-Z0-9._-]+`)
+
+// TestReadmeDockerImageReferencesAreConsistent ensures every README mentions
+// the same, currently published Docker image name. A partial rename, where
+// one example is updated but another is missed, would otherwise leave users
+// copying a command that pulls a nonexistent image.
+func TestReadmeDockerImageReferencesAreConsistent(t *testing.T) {
+	for _, path := range []string{"../README.md", "../README.zh-cn.md", "../README.zh-tw.md"} {
+		t.Run(filepath.Base(path), func(t *testing.T) {
+			content, err := os.ReadFile(path)
+			if err != nil {
+				t.Fatal(err)
+			}
+			references := dockerImageReference.FindAllString(string(content), -1)
+			if len(references) == 0 {
+				t.Fatalf("no docker.gitea.com image reference found in %s", path)
+			}
+			for _, ref := range references {
+				if ref != publishedDockerImage {
+					t.Errorf("found image reference %q in %s, want %q", ref, path, publishedDockerImage)
+				}
+			}
+		})
+	}
+}
+
 // toolInfo is what TestReadmeToolTables tracks per tool, both as registered
 // in code and as documented in a README, so the two can be compared.
 type toolInfo struct {