You do not need to keep the .dmg after you have installed the app. They can be tossed without issue. Particularly if it is a drag and drop app.
If it is one of those apps that come with their own installer and uninstaller, you can toss the .dmg if the uninstaller is also installed. If the uninstaller, remains as a part of the .dmg, then I would suggest keeping it.
Next we'll get someone saying they tossed the .dmg and their program disappeared. Well, that's because you didn't install the app. After you open that .dmg, you need to drag and drop the app's icon into your Application folder. Now it's installed and now you can delete the .dmg.