Incorrect output while comparing two strings C++

I have class CPerson that in simple looks like this:

CPerson
{
public:
   CPerson();
   pair<string, string> CP_surname_name;
   vector<CCar> CP_CarList;
};

then I have a vector<CPerson> CR_people It's sorted vector by pair CP_surname_name. The problem is, when I need to compare surname and name, inputted by user firstly I go throug vector, if there is already the person I am looking for.

auto it = lower_bound(CR_people.begin(), CR_people.end(), surname_name);

I have overriden operator< so sorting is fine. But when I need to check, if the surname_name is exact the same as CP_surname_name by:

if(surname_name == (*it).CP_surname_name){...}

it gives me falseeven they are same. I already tried:

if(surname_name.first == (*it).CP_surname_name.first && surname_name.second == (*it).CP_surname_name.second){...}

and it works the same. I also tried strcmp() but it gives me errors, because I am using string, not char* so I tried append .c_str() to retype it, and that gave me also wrong results. The compare() in String class did not work as well. Thanks for any help, and sorry for my bad english.