Using the if statement with the Serial monitor

This works for me: ie, I got hello when I pretended to be Max. It's your code from #2 with the = replaced with == as explained.

(Format tidied up a bit)

String myname = "";

void setup()
{
  Serial.begin(9600);
}

void loop() {

  Serial.println("Enter your name.");

  while (Serial.available() == 0)
  { //Wait for user input

  }
  myname = Serial.readString();

  if (myname == "Max")
  {
    Serial.println("hello");
  }
  else
  {
    Serial.println("wut");
  }
}