diff --git a/lib/util/Components.js b/lib/util/Components.js
index dec1143162..7abfbee72f 100644
--- a/lib/util/Components.js
+++ b/lib/util/Components.js
@@ -517,6 +517,47 @@ function componentRule(rule, context) {
           return undefined;
         }
 
+        // case: any = () => () => null
+        if (node.parent.type === 'ArrowFunctionExpression' && node.parent.parent.type === 'AssignmentExpression' && !isPropertyAssignment && utils.isReturningJSXOrNull(node)) {
+          if (isFirstLetterCapitalized(node.parent.parent.left.name)) {
+            return node;
+          }
+          return undefined;
+        }
+
+        // case: { any: () => () => null }
+        if (node.parent.type === 'ArrowFunctionExpression' && node.parent.parent.type === 'Property' && !isPropertyAssignment && utils.isReturningJSXOrNull(node)) {
+          if (isFirstLetterCapitalized(node.parent.parent.key.name)) {
+            return node;
+          }
+          return undefined;
+        }
+
+        // case: any = function() {return function() {return null;};}
+        if (node.parent.type === 'ReturnStatement') {
+          if (isFirstLetterCapitalized(node.id && node.id.name)) {
+            return node;
+          }
+          const functionExpr = node.parent.parent.parent;
+          if (functionExpr.parent.type === 'AssignmentExpression' && !isPropertyAssignment && utils.isReturningJSXOrNull(node)) {
+            if (isFirstLetterCapitalized(functionExpr.parent.left.name)) {
+              return node;
+            }
+            return undefined;
+          }
+        }
+
+        // case: { any: function() {return function() {return null;};} }
+        if (node.parent.type === 'ReturnStatement') {
+          const functionExpr = node.parent.parent.parent;
+          if (functionExpr.parent.type === 'Property' && !isPropertyAssignment && utils.isReturningJSXOrNull(node)) {
+            if (isFirstLetterCapitalized(functionExpr.parent.key.name)) {
+              return node;
+            }
+            return undefined;
+          }
+        }
+
         // for case abc = { [someobject.somekey]: props => { ... return not-jsx } }
         if (node.parent && node.parent.key && node.parent.key.type === 'MemberExpression' && !utils.isReturningJSX(node) && !utils.isReturningOnlyNull(node)) {
           return undefined;
diff --git a/tests/lib/rules/display-name.js b/tests/lib/rules/display-name.js
index ba4b9181fe..841af839fc 100644
--- a/tests/lib/rules/display-name.js
+++ b/tests/lib/rules/display-name.js
@@ -615,6 +615,34 @@ ruleTester.run('display-name', rule, {
         };
       `,
     },
+    {
+      // issue #3346
+      code: `
+        demo = () => () => null;
+      `,
+    },
+    {
+      // issue #3346
+      code: `
+        demo = {
+          property: () => () => null
+        }
+      `,
+    },
+    {
+      // issue #3346
+      code: `
+        demo = function() {return function() {return null;};};
+      `,
+    },
+    {
+      // issue #3346
+      code: `
+        demo = {
+          property: function() {return function() {return null;};}
+        }
+      `,
+    },
     {
       // issue #3303
       code: `
@@ -1141,5 +1169,33 @@ ruleTester.run('display-name', rule, {
         },
       ],
     },
+    {
+      code: `
+        Demo = () => () => null;
+      `,
+      errors: [{ messageId: 'noDisplayName' }],
+    },
+    {
+      code: `
+        demo = {
+          Property: () => () => null
+        }
+      `,
+      errors: [{ messageId: 'noDisplayName' }],
+    },
+    {
+      code: `
+        Demo = function() {return function() {return null;};};
+      `,
+      errors: [{ messageId: 'noDisplayName' }],
+    },
+    {
+      code: `
+        demo = {
+          Property: function() {return function() {return null;};}
+        }
+      `,
+      errors: [{ messageId: 'noDisplayName' }],
+    },
   ]),
 });