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For setting the name of an existing anonymous function:
(Based on @Marcosc's answer)

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();
console.log(fn()); // —> true

Demo.

Note: Don't do it ;/

For setting the name of an existing anonymous function(based on Marcosc's answer):

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();
console.log(fn()); // —> true

Demo.

Note: Don't do it ;/

For setting the name of an existing anonymous function:
(Based on @Marcosc's answer)

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();
console.log(fn()); // —> true

Demo.

For setting the name of an existing anonymous function:
(Based on @Marcosc's answer)

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();
console.log(fn()); // —> true

Demo.

Note: Don't do it ;/

For setting the name of an existing anonymous function:
(Based on @Marcosc's answer)

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();

Demo.

For setting the name of an existing anonymous function:
(Based on @Marcosc's answer)

var anonymous = function() { return true; }
var name = 'someName';
var strFn = anonymous.toString().replace('function ', 'return function ' + name);
var fn = new Function(strFn)();
console.log(fn()); // —> true

Demo.