Can I get the currently opened ASP page file name in Visual Studio.NET in a custom control?

It CAN be done. See here: http://weblogs.asp.net/gunnarpeipman/archive/2008/05/21/using-parent-page-properties-in-user-control.aspx

but even this page starts out by saying

this situations is a warning sign - there's something wrong with UI structure if user controls should know their parents.

If you need to know information about the page, then a better approach is to create a property on your control that you can set from the page. Then from within the control, you can check the value of the property.

For example, if you REALLY need to know the page name, then your control should have a property called "PageName", and then when you ad it to your page, you can set the property explicitly. (I'll come back with an example if you like).

Here's an example I ran across - a date-time chooser control for a reporting page. It has a property called FromDate that is tied to a text box.

public  DateTime FromDate
{
    get
    {
        return Convert.ToDateTime(txtFrom.Text);
    }
    set
    {
        txtFrom.Text = value.ToString();
    }
}

Then you would set it int he page like this:

<uc1:DateRangeControl ID="DateRangeControl1" runat="server" 
                FromDate="1/1/2009"    />

The reason we say it's a design flaw is that good OO design would say that a control by nature should be able to operate without knowing what container it is in.

Why do you need this information at design-time? If you're having problems with it displaying correctly in design-mode, could you instead check the DesignMode property and only execute the page-dependent logic at runtime?

I agree that if you need to do this, then there's probably something wrong with the UI design. However, I've found it useful on occasion.

Assuming your custom control extends WebControl or one of its subclasses and is inside a Page:

string myPageName = System.IO.Path.GetFileName(this.Page.Request.Path);

Easy as that.