You can use a third party app like Handcent, this has many more settings to play with than the standard app. You need to look in Settings>Notification Settings and then Notification Settings again. Also Popup settings too can be tweaked so that you get the display to show what you want.
GoSMS is another that I have heard is very good and as both are free from the Android Market you could download them and have a play. If you decide to keep one you just need to turn off the notifcations in the stock app otherwise you will get two for each text that comes in.
