I know what your problem is, more or less. The issue is you want to have all of your managing devices (router, pihole, Fing, whatever that is...) display identical hostnames. I've got it to work on my setup but its not as easy as I think it should be.
The problem is that hostnames don't propagate from one managing device to another. The answer is that you have to manually configure each of your managing devices with the same information. I haven't uncovered why this information isn't automatically shared from, say the gateway router to the other devices. Maybe there's a good security reason or maybe nobody has taken on the task.
To make this work I first set my gateway router as the DHCP server and used its web interface to set up static ips and hostnames by mac address for all of the devices.
Then, on the pihole, I edited two files by hand. Keep in mind that there may be some sloppiness here, I'm new-ish to linux and networking.
File 1) Made a new file called /etc/hosts.hom in which I included the same IP/hostname information that I did on the router. Each entry should follow this simple format:
ipaddress hostname
so
192.167.17.90 dentarthurdent
Note that the mac address isn't necessary since the router is the one giving out IP addresses. This file just tells the pihole what name to use based on the IP address given out by the router.
File 2) made a new file -- /etc/dnsmasq.d/99-overrides and put these lines in it:
addn-hosts=etc/hosts.hom
domain=hom
local=/hom/
Of course, if you don't care about specifying a lan domain you can ignore lines two and three. I think. (If you do care, you'll have to set up the domain name on each device...) The main thing is that pihole reads and runs all of the files in /etc/dnsmasq.d/ and it will therefore obligingly load the hostnames and whatnot from whatever file you tell it to with the addn-hosts=xxx bit. Hosts.hom could be Pangalatic.Gargleblaster if I understand.
You'll have to decide if its worth it to learn how to tailor your Fing device with this information. If its not possible in the app itself I bet its possible to configure your phone's OS to use those specific hostnames. I'd bet more if it was android, very little if its an Iphone. But I don't know. Good luck. 
EDIT:
It just occurred to me that I complicated things but for a reason. I think you could technically edit just one file on the pi: /etc/hosts
I did it the long way because since I've been at this, I've seen that file altered and overwritten. This way I know my edits will remain intact.