Help with applescript window image

One can reference a custom icon, where it is a System icon, or your own custom 512x512 .icns icon in AppleScript as the following:

property app_icon : "/System/Library/CoreServices/CoreTypes.bundle/Contents/Resources/MultipleItems Icon.icns"

display dialog "some msg" with title "Test dialog panel" with icon POSIX fileapp_icon as alias

Or as red_menace pointed out via AppleScript/ObjC, one can considerably extend the Alert dialog:

I have complete control over the icon, informational, and message text fonts, and the green panel is a horizontally scrolling text view. In this case, it was a brief amount of AppleScript that calls a Python/Objective-C handler. Based on whether the return address contains valid Apple domain, or subdomains, the alert changes its icon, its text, and the scrolling text view changes its background color.

Are you talking about an alert dialog, or some other kind of window? It looks like that is display alert from Standard Additions, which doesn't let you set an icon, but you can set one with display dialog (and NSAlert using AppleScriptObjC).