You almost certainly don't want to do this. A caller should never know who is calling it. Instead, the difference between the two callers should be abstracted into a parameter, and passed into the method being called:
private void doSomething(bool doItThisWay)
{
if (doItThisWay)
{
// Do it one way
}
else
{
// Do it the other way
}
}
private void method1()
{
doSomething(true);
}
private void method2()
{
doSomething(false);
}
This way, if you add a method3, it can either doSomething one way or the other, and doSomething won't care.