A good way to not break any existing code would be to chain the new method name to the old in a such as

private void MyNewMethodName() { TheOldMethodName(); } 

and then mark the old method as obsolete (if your language support this). This way any existing code will still work and you can gradually take out all the old spelling mistake out of your code base. Eventually you could even copy/paste the method body into the new method and delete the old one.

A good way to not break any existing code would be to chain the new method name to the old in a such as

private void MyNewMethodName() { TheOldMethodName(); } 

and then mark the old method as obsolete (if your language support this). This way any existing code will still work and you can gradually take out all the old spelling mistake out of your code base. Eventually you could even copy/paste the method body into the new method and delete the old one.

/Edit As ivo said in the comment : An even better thing to do would be to move the code from TheOldMethodName into the MyNewMethodName and call the new method from the old one. This one would also have the advantage to help the dev to get their head around where the code belong to.