Do you both have a yosemite computer in the network.. can you please check if it is also incrementing its share name to the network??
I placed a yosemite computer in my network.. and it immediately went nuts with everything incrementing continually.. not just the computer with Yosemite but the entire works.
There is a major DNS bug and so far the fixes are kind of hack jobs eg.
http://arstechnica.com/apple/2015/01/why-dns-in-os-x-10-10-is-broken-and-what-yo u-can-do-to-fix-it/
Some of it is caused by peer to peer wireless swapping now involved.. although I am not sure how the ATV is involved.
I can suggest you do a full factory reset to the AE..
The best way to test is full factory reset.
Factory reset universal
Power off the AE.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the AE to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
Then redo the setup from the computer with Yosemite.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg AEgen5 and AEwifi for basestation and wireless respectively.
Even better if the issue is more wireless use AE24ghz and AE5ghz with fixed channels as this also seems to help stop the nonsense.
2. Use all passwords that also comply but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
3. Ensure the AE always takes the same IP address.. this is not a problem for AE as router but bridged you need to make this happen on the main router using dhcp reservations.
4. Check your share name on the computer is not changing.. make sure it also complies with the above.. short no spaces and pure alphanumeric.. Same with ATV and any other devices..
5. Make sure IPv6 is set to link-local only in the computer. For example wireless open the network preferences, wireless and advanced / TCP/IP.. and fix the IPv6. to link-local only. This is not relevant to iOS devices where the controls are preconfigured.
