Q:

How do I call a member function that has the same name as another? 

I need two member functions with the same name "functionName" in className class.  Like this..
className::functionName(BaseClass &object)
{
    //do something here with object
}
className::functionName(SecondBaseClass &object2)
{
    //do something here with object2
}

So, If I have two functions with the same name, how do I call the one that I want? 

A:

This is called function overloading.  It picks one depending on the type of the parameter, but it will fail to compile if the parameter you want to pass could reasonably convert to more than one overload. 
If your parameter is derived from both base classes, try the following to disambiguate it 
functionName(static_cast<DesiredBase&>(myobject));

