Notification Center message via AppleScript/osascript -- specify an application name and icon
I don't think it's possible with AppleScript but it is with terminal-notifier:

-sender ID         The bundle identifier of the application that should be
shown as the sender, including its icon.
-appIcon URL       The URL of a image to display instead of the application
icon (Mavericks+ only)


For example:

terminal-notifier -title title -message message -sender com.apple.TextEdit