Have you had functions yet? They make it easier to keep the program in "neat pieces".
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// work() asks details and reports the pays
void work( const string& name, char type );
int main ()
{
string n;
cout << "Enter your Name:";
getline(cin,n);
while ( true ) {
cout << "Are you a Part-time or Fulltime employee? [P/F]";
char t;
cin >> t;
work( n, t );
}
}
Note though that this program repeats forever, which probably is not a good thing.
typically you validate user input asap after getting it, rather than do a bunch of stuff and then circle back and start over (this will annoy the user!).
roughly, then, consider (pseudocode)
do
cout enter p/f
cin t
t = toupper(t);
while(t != 'F' && t != 'P')