Without jQuery :
var value = document.getElementById('nameValidation').value;
The syntax you had would be usable to get an input by its name, not its id.
If what you want is to use this value when it changes, you can do that :
var nameValidationInput = document.getElementById('nameValidation');
function useValue() {
var NameValue = nameValidationInput.value;
// use it
alert(NameValue); // just to show the new value
}
nameValidationInput.onchange = useValue;
nameValidationInput.onblur = useValue;