diff --git a/lib/rules/multi-word-component-names.js b/lib/rules/multi-word-component-names.js
index 4e4e7db28..6f73de294 100644
--- a/lib/rules/multi-word-component-names.js
+++ b/lib/rules/multi-word-component-names.js
@@ -60,7 +60,7 @@ module.exports = {
         ignores.add(casing.kebabCase(ignore))
       }
     }
-    let hasVue = false
+    let hasVue = utils.isScriptSetup(context)
     let hasName = false
 
     /**
diff --git a/tests/lib/rules/multi-word-component-names.js b/tests/lib/rules/multi-word-component-names.js
index 6c1e852b6..d11b11d3f 100644
--- a/tests/lib/rules/multi-word-component-names.js
+++ b/tests/lib/rules/multi-word-component-names.js
@@ -204,7 +204,7 @@ tester.run('multi-word-component-names', rule, {
       `
     },
     {
-      filename: 'test.vue',
+      filename: 'MultiWord.vue',
       code: `
       <template>
         <AppButton />
@@ -329,8 +329,8 @@ tester.run('multi-word-component-names', rule, {
       </script>`,
       errors: [
         {
-          message: 'Component name "Item" should always be multi-word.',
-          line: 3
+          message: 'Component name "test" should always be multi-word.',
+          line: 1
         }
       ]
     }