diff --git a/source-map-support.d.ts b/source-map-support.d.ts
index d8cb9d8..21c1055 100755
--- a/source-map-support.d.ts
+++ b/source-map-support.d.ts
@@ -50,6 +50,13 @@ export interface Options {
      * @param options options object internally passed to node's `_resolveFilename` hook
      */
     onConflictingLibraryRedirect?: (request: string, parent: any, isMain: boolean, options: any, redirectedRequest: string) => void;
+
+    /**
+     * If enabled, will fallback to getting mapped function name from callsite (from the following stack frame) when neither
+     * enclosing position nor runtime have a function name.
+     * Default: true
+     */
+    callsiteFallback?: boolean;
 }
 
 export interface Position {
diff --git a/source-map-support.js b/source-map-support.js
index ad830b6..5c48b36 100644
--- a/source-map-support.js
+++ b/source-map-support.js
@@ -92,6 +92,10 @@ var sharedData = initializeSharedData({
   // If true, the caches are reset before a stack trace formatting operation
   emptyCacheBetweenOperations: false,
 
+  // If true, will fallback to getting mapped function name from callsite (from the following stack frame) when neither
+  // enclosing position nor runtime have a function name.
+  callsiteFallback: true,
+
   // Maps a file path to a string containing the file contents
   fileContentsCache: Object.create(null),
 
@@ -554,6 +558,14 @@ function cloneCallSite(frame) {
   return object;
 }
 
+// Fix position in Node where some (internal) code is prepended.
+// See https://github.com/evanw/node-source-map-support/issues/36
+// Header removed in node at ^10.16 || >=11.11.0
+// v11 is not an LTS candidate, we can just test the one version with it.
+// Test node versions for: 10.16-19, 10.20+, 12-19, 20-99, 100+, or 11.11
+const noHeader = /^v(10\.1[6-9]|10\.[2-9][0-9]|10\.[0-9]{3,}|1[2-9]\d*|[2-9]\d|\d{3,}|11\.11)/;
+const headerLength = isInBrowser() ? 0 : (noHeader.test(process.version) ? 0 : 62);
+
 function wrapCallSite(frame, state) {
   // provides interface backward compatibility
   if (state === undefined) {
@@ -577,31 +589,31 @@ function wrapCallSite(frame, state) {
 
     var line = frame.getLineNumber();
     var column = frame.getColumnNumber() - 1;
-
-    // Fix position in Node where some (internal) code is prepended.
-    // See https://github.com/evanw/node-source-map-support/issues/36
-    // Header removed in node at ^10.16 || >=11.11.0
-    // v11 is not an LTS candidate, we can just test the one version with it.
-    // Test node versions for: 10.16-19, 10.20+, 12-19, 20-99, 100+, or 11.11
-    var noHeader = /^v(10\.1[6-9]|10\.[2-9][0-9]|10\.[0-9]{3,}|1[2-9]\d*|[2-9]\d|\d{3,}|11\.11)/;
-    var headerLength = noHeader.test(process.version) ? 0 : 62;
-    if (line === 1 && column > headerLength && !isInBrowser() && !frame.isEval()) {
+    if (line === 1 && column > headerLength && !frame.isEval()) {
       column -= headerLength;
     }
-
     var position = mapSourcePosition({
       source: source,
       line: line,
       column: column
     });
+
     state.curPosition = position;
+    const nextPosition = state.nextPosition;
+
     frame = cloneCallSite(frame);
+
+    // Check for function name in this order:
+    // runtime function name, then fallback to callsite (subsequent stack frame's position)
     var originalFunctionName = frame.getFunctionName;
     frame.getFunctionName = function() {
-      if (state.nextPosition == null) {
-        return originalFunctionName();
+      const originalName = originalFunctionName();
+      if(originalName != null) return originalName;
+      if (sharedData.callsiteFallback && nextPosition != null) {
+        const nextPositionName = nextPosition.name;
+        if(nextPositionName != null) return nextPositionName;
       }
-      return state.nextPosition.name || originalFunctionName();
+      return null;
     };
     frame.getFileName = function() { return position.source; };
     frame.getLineNumber = function() { return position.line; };
@@ -895,6 +907,10 @@ exports.install = function(options) {
       shimEmitUncaughtException();
     }
   }
+
+  if (typeof options.callsiteFallback === 'boolean') {
+    sharedData.callsiteFallback = options.callsiteFallback;
+  }
 };
 
 exports.uninstall = function() {
diff --git a/test.js b/test.js
index 7dabc6c..7c870ae 100644
--- a/test.js
+++ b/test.js
@@ -598,20 +598,21 @@ it('finds the last sourceMappingURL', async function() {
 it('maps original name from source', async function() {
   var sourceMap = createEmptySourceMap();
   sourceMap.addMapping({
-    generated: { line: 2, column: 8 },
+    generated: { line: 3, column: 8 },
     original: { line: 1000, column: 10 },
     source: `.original-${id}.js`,
   });
   sourceMap.addMapping({
-    generated: { line: 4, column: 0 },
+    generated: { line: 5, column: 0 },
     original: { line: 1002, column: 1 },
     source: `.original-${id}.js`,
     name: "myOriginalName"
   });
   await compareStackTrace(sourceMap, [
-    'function foo() {',
+    'function identity(v) { return v }',
+    'const foo = identity(function () {',
     '  throw new Error("test");',
-    '}',
+    '})',
     'foo();'
   ], [
     'Error: test',