Newly installed programs always appear with external drives in Finder
When you download an application, it often comes inside a "Disk image" (a .dmg file). This is a virtual volume, which appears just like other disks on your Desktop, once you've launched it.

You have to copy the application from there into your /Applications folder. (Disk images often contain an alias to your Applications folder, so you can easily drop the app onto the folder.
Or, if the image contains an installer app or package, you have to run the installer app.

Once you have done this, you can eject the disk image and trash the .dmg file. If you haven't copied the app or installed it, then you need to make sure this is done first.