Hey everyone, I have spent the last few hours solving this on my own as there have been many issues with upgrading old iPhones to new ones using the restore from backup feature and subsequently changing your device name as it will be set to the old backups name by default.
Here are the steps to follow that worked for me and should work for you, it's easier than you may think (by the way read on after this issue because there may be more information I provide that works for other issues associated with this one).
Before I go into the steps let me make sure that you have the following problem... You have an iPhone lets say device "A" and a new iPhone device "B" with two separate names and showing up correctly in the iTunes window as well as on the iPhone itself (general > about > name). If this is true and the only problem remains is that in the "manage devices" list in iTunes under "account info" there are two separate devices with the same name listed as device "A". If this is true follow the steps below.
1. Make sure you have a single backup for each device (go to the iTunes application on your desktop and open "iTunes" then press "preferences..." then "devices" where you should see a single backup under the preferred name, if not simply backup your devices and delete everything but the most current backup). Also make sure that your devices are correctly named either through iTunes when connected via usb or wifi, or through the iPhone itself under (general > about > name).
2. If you have more than one backup per device simply sync the device and once a new backup has been created, delete the ones with the older date as they will no longer be relevant (this step may be skipped however this is what I did so you might want to do it as it will clean up your backup history and create a recent backup).
3. Using iTunes remove both device "A" and device "B" (they should be listed under the same name device "A" as stated before and probably seem like a duplicate however, remove both).
4. To re-associate device "A" simply open settings scroll down to "iTunes & App Store" click on it and switch on "Music" under the heading "Automatic downloads" (remember this process works for all iDevices and can also be done through the iTunes and App Store apps located on that specific iDevice. More information is available on re-assocaiting devices can be found here View and remove associated devices in iTunes - Apple Support).
5. Now you will want to check to make sure the device has been re-associated by simply accessing your account info on iTunes and pressing "manage devices", there should be device "A" in the list, if not you either did not follow step 4 correctly or you have yet to update the list. To update the list simply press "done" and it will take you back to the previous page on your iTunes application on your desktop, from there you may "manage devices" once again and it should appear (note I never had problems with this step so it may be reliant on your wifi/ethernet connection from your devices as they must be able to sync to apple's servers to show the newly associated device).
6. Now you will likely try to jump ahead of me and repeat steps 4 and 5 for device "B" however, DO NOT do this just yet. First you will want to sign out of your apple ID on device "B" as this is where the problem lies (your new device "B" has synced with iTunes and associated itself using your old name for device "A" before you could rename it and thus created a problem where the device may be named device "B" however, the apple ID has the original device "A" stamp on it when associated to your apple ID).
7. Once you have signed out make sure that device "B" has the name you wish to be associated on iTunes then simply sign back in to your apple ID on that device once more and follow the steps you used for associating your device as stated above in parts 4 and 5 .
If all goes as planned and you followed all these steps (seems like a lot more work in writing than it actually is) you should see device "A" and device "B" in your iTunes (if connected) and they will now most likely have the correct names associated with the device in "manage devices" section under "account info" in iTunes. Hope this helped 🙂
OTHER PROBLEMS RELATED TO THIS ISSUE COVERED BELOW (YOU MAY WANT TO TAKE A LOOK JUST IN CASE)
Some other problems that occurred when making sure all 4 of my iPhones had separate names on both the iTunes widow and on the device itself as well as the associated device section under "manage devices" in account info" on iTunes. I also ran into the problem that these overlapping names caused issues with wifi syncing and with their ability to correctly update settings without being stuck at "waiting for changes to be applied" or where the sync performs and it still indicates that changes need to be applied rather than simply syncing the device. Anyways, the easiest way to tackle all of these at once is...
1. Make sure all your devices (I had 4 separate iPhones) are currently in a state where you would be comfortable restoring them (i.e. you aren't missing any information from your last sync or have anything to lose by deleting backups on your computer).
2. (Note: this step requires you to delete your iDevice backups within iTunes, if you are uncomfortable doing so I suggest you do a backup of your computer running iTunes with the backups so that you may restore everything to the original if problems do occur however, this process will take approximately 10 minutes per device and I highly doubt your iPhone will fail during those 10 minutes but, better safe than sorry) Once you are comfortable with that, delete all your backups that have been created on your iTunes by opening "iTunes" then pressing "preferences..." then "devices". In this section you will find all of your backups for each iPhone with the names you created on each device.
3. From there simply reconnect your oldest iPhone and press backup, wait until this process finishes and repeat for every device you have. You should now have 1 backup for each device under the correct name you created. If no, please make sure you followed the steps above correctly however, this problem never occurred when I followed this process.
4. Now that you have a single backup for each device and all devices synced to the most current backup state you will have to find the iPhone that are causing the issues. (In my case I had an iPhone 3GS, 4S, 5S, and 6S and the 4S would never appear under the list of iPhone connected to my network unless I plugged it directly into my computer. However, I knew the problem wasn't my wifi so I deduced that the problem must've been from an overlapping device association "see part 1 above". Since the problem was derived from these devices I put aside my 3GS and 6S to make the situation less daunting. Now using my iPhones 4S and 5S I simply turned off my 5S which allowed my older 4S under apparently the same identification in iTunes yet separately named, to access my iTunes via wifi, from there I simply synced via wifi and turned on my 5S again to remove the problems of competing devices.
This may be less helpful as this was a very specific issue however, I hope you could follow along and learn something from it. Basically, when you get a new iPhone and restore from a backup and rename the device in iTunes. iTunes may recognize the device as the older name even though to you it visibly states something else. Because of this you must manually re-associate the competing devices so that iTunes can recognize them as separate, unique iPhones rather than competing "clone" backups with separate device names.
