Even if I give the right Input it still showing the error alert message

This is the code

<div class="form-group"><input id="name" type="text" placeholder="Name" name="name" ></div> <button type="submit" class="btn btn-primary signupbtn" onclick="check()">Sign Up</button>

`

let first = document.getElementById('name');



function check() {
  var pattern = /^[a-zA-Z]+$/;
  var res = pattern.test(first.value);
  
  if(first.value != res){
    alert('Invalid First Name');
  } 
  
}

`

I have tried keeping (first.value = res) and then executing. This time it is giving alert message only when there is correct input but not when wrong input. But as keep (first.value != res) then it is showing error message every time I press the signup button.