The file is on your iPad 7 times. Each time you select "Open with Filemaker go" in Dropbox the files is copied to filemaker go. Filemaker Go does not delete the file automatically to protect your data. You will have to delete the files from Filemaker Go manually.
To delete files from Filemaker GO.
Under Files on device in Filemaker Go Slide your finger from right to left on the right edge of the Filemaker Box, next to the databases that needs deleted. A red Delete box will show on screen then press delete.
Filemaker Go is not designed to sync with Dropbox.
There are no other versions of the app listed under Files on Device. Although there has been many versions previously and I always delete them..... Sometimes while attached to itunes and sometimes on the ipad itself. Could there be something else?
I tested on my iPad and I didn't have any problems. The first time I open the file it copy with same title, without deleting the titIe I open the file a second time from the dropdox and it append a 2 to the end of the file then open the file. I then delete both files and then openned again from Dropbox and the file copied correctly with no numbers appended.
Verify that you are using the newest version of Filemaker Go. I'm using 12.0.7. Verify you are using the newest version of Dropbox, I just downloaded to test. I'm using 2.2.2. both on an iPad 3.
You may also want to verify that the files are not in Go from iTunes.
Just for information purposes, incase another user come across this post at a later date. I tested with Sugarsync another file sharing service. From within Sugarsync if you open your databases with the Open with option the file name changes. If you sync the databases to your iPad first, then use the "open with" option in sugarsync (from the sync folder) the filename stays the same.
I am running the same items as you except i have an iPad 2. I tested a small database and it worked like it was supposed to. However I'm still having the same issue with my main app. Funny thing is when I open FMGO and add up the sizes of the databases there it comes out to about 2 GB. When I go to Settings-General-Usage on the ipad it shows 7.1 GB. Im wondering why there is a difference and could that be part of my problem. I'm sure part of it is FMGO itself.
Have you deleted and reinstalled Filemaker Go? I don't know why, but there has been a few issues fixed by reinstalling GO. Maybe because Filemaker GO 12 is a fairly new product.