How to get position of a certain element in strings vector, to use it as an index in ints vector?

To get a position of an element in a vector knowing an iterator pointing to the element, simply subtract v.begin() from the iterator:

ptrdiff_t pos = find(Names.begin(), Names.end(), old_name_) - Names.begin();

Now you need to check pos against Names.size() to see if it is out of bounds or not:

if(pos >= Names.size()) {
    //old_name_ not found
}

vector iterators behave in ways similar to array pointers; most of what you know about pointer arithmetic can be applied to vector iterators as well.

Starting with C++11 you can use std::distance in place of subtraction for both iterators and pointers:

ptrdiff_t pos = distance(Names.begin(), find(Names.begin(), Names.end(), old_name_));