[ОлегА]

function name_hide(val){
    
    if(val.length > 1){        
        document.getElementById('name').style.display = 'none';            
    } else if(! val.length){
        document.getElementById('name').style.display = 'inline';
    }
    
}

<form name="forma" action="test.html1" method="POST">
<label>Ваше имя: </label><br />
<input id="name_txt" type="text" onkeyup="name_hide(this.value);" name="name" />
<span id="name">Введите Ваше имя!</span>
<br /><br />
<input type="submit" />
<br /><br />
</form>