yes it is possible. In the code behind of the control declare a public property like,
private string filename= string.Empty;
public string FileName
{
get
{
return this.filename;
}
set
{
this.filename = value;
}
}
And now you might use this property to your control like
<crt:mycontrol id="crt" filename="MyTestFileName" xmlns:crt="#unknown"> </crt:mycontrol>