You are saving the session data with
Session["frugt_navn"]
So that doesn't seem to be the problem :-)
I do not believe you can reuse this session data in the aspx page (anyway, I don't know how to do that). Try this:
private int Value = 0;
private string frugt_navn;
protected void Page_Load(object sender, EventArgs e)
{
Panel_visfrugt.Visible = true;
Panel_vis.Visible = false;
frugt_navn = (string)Session["frugt_navn"];
}
After doing this in the Page_Load you can use the value of the global variable. It should also be possible to use this variable (I've done that before) in your aspx but I cannot find an example right now. I remember you should at least make it public then.