Hm, why the change of all _domain to domain, not the other way around?
The _xyz naming of argument variables has been seen usually when it was needed to create a copy of the argument in the implementation, because e.g. the const-refness was in the way. As the normal naming of arguments and variables is without the _ prefix,. The prefix is then used with the argument name to denote this is the input to the actual variable then used in the implementation.

So:

void foo(const Type arg)
 {
    // need to do non-const things with arg value, meh
}

->

void foo(const Type _arg)
 {
    Type arg(_arg);
    // do non-const things with arg value
}