C++ inherit from multiple base classes with the same virtual function name

A function overrides a virtual function of a base class based on the name and parameter types (see below). Therefore, your class C has two virtual functions foo, one inherited from each A and B. But a function void C::foo() overrides both:

[class.virtual]/2

If a virtual member function vf is declared in a class Base and in a class Derived, derived directly or indirectly from Base, a member function vf with the same name, parameter-type-list, cv-qualification, and ref-qualifier (or absence of same) as Base::vf is declared, then Derived::vf is also virtual (whether or not it is so declared) and it overrides Base::vf.

As I already stated in the comments, [dcl.meaning]/1 forbids the use of a qualified-id in the declaration of a (member) function:

When the declarator-id is qualified, the declaration shall refer to a previously declared member of the class or namespace to which the qualifier refers […]”

Therefore any virtual void X::foo(); is illegal as a declaration inside C.

The code

class C : public A, public B
{
    virtual void foo();
};

is the only way AFAIK to override foo, and it will override both A::foo and B::foo. There is no way to have two different overrides for A::foo and B::foo with different behaviour other than by introducing another layer of inheritance:

#include <iostream>

struct A
{
    virtual void foo() = 0;
};

struct B
{
    virtual void foo() = 0;
};

struct CA : A
{
    virtual void foo() { std::cout << "A" << std::endl; }
};

struct CB : B
{
    virtual void foo() { std::cout << "B" << std::endl; }
};

struct C : CA, CB {};

int main() {
    C c;
    //c.foo();  // ambiguous

    A& a = c;
    a.foo();

    B& b = c;
    b.foo();
}