Testing ID and Serial Communication (Update)
You are assigning a string to a single character here.


  char myID = 'tg123';


Instead you should make it a String variable. And compare it after all the characters are recieved.


  String myID = "tg123";


And Here is the modified code you should test with. In this case I have assumed you simply write the ID (string) in serial terminal and hit enter. 

N.B. If you want to enter each character one by one, then it will not be able to catch the whole string. For this case you have to add some time-out to wait for next character to arrive.

String recvData = "";
void loop()
{    
  while (!Serial.available());
  while (Serial.available())
  { 
    char ch = Serial.read();
    recvData += ch;
  }
  if (myID == recvData)
  {
    digitalWrite(gLED, HIGH);
    digitalWrite(rLED, LOW);
    Serial.println("Hello! Your name is Trevor.");
    delay(5000);
  }
  else
  {
    digitalWrite(rLED, HIGH);
    digitalWrite(gLED, LOW);
    Serial.println("Invalid ID! Try again.");
    delay(2000);
  }
  recvData = "";
 }