We will change the name and all the icons.
While you're at it, you'll also want to create a proper Info.plist and icon file for Mac, two things that Lazarus can't create.
Open the app's .ico file in Preview and copy it to the clipboard. Then open Icon Composer and paste the image into the appropriate size class (eg, 128 x 128). Save as an .icns file.
Since you're already working around Lazarus limitations with a script, just add copying of the .icns file into the .app bundle to the script, eg, cp -p MyApp.icns MyApp.app/Contents/Resources.
Now make a copy of the useless, generic Info.plist that Lazarus creates for the .app bundle and edit it. Add something like this to activate the icon:
<key>CFBundleIconFile</key>
<string>MyApp.icns</string>
Add to your script to copy this file too, eg, cp -p Info.plist MyApp.app/Contents .
You'll also want to change the bundle ID in the Info.plist. The bundle ID is how macOS identifies the app. By default, the bundle ID that Lazarus creates will be something like com.company.MyApp. You definitely don't want that floating around as your bundle ID.
You can adjust many other settings in Info.plist, for example the app's version. That way if anyone selects the app in Finder and presses Cmd+I to get info on the app, the popup will display the correct version, rather than the default version that Lazarus assigns your app (0.1).