By writing the script to handle the event, one example will be:
<script>
function CheckTextLength(element, minLength){
if(element.value.length < minLength){
alert("Too short!");
return false;
}
}
</script>
and your asp.net control:
<asp:TextBox ID="txt_Cat_Name" onChange="CheckTextLength(this,15)" runat="server" CssClass="Text"></asp:TextBox>