You simply need to add an entry to your host file. Then you'll be able to use a DNS name to access it. The following command will do what you want:
echo "192.168.2.10 homeapp" >> /etc/hosts
You'll need to do this on each client that you'll be accessing this site from. For Windows clients it will be very similar:
ECHO "192.168.2.10 homeapp" >> %System32%\Drivers\etc\hosts
Yes, your tablets and smart phones will also (generally) have a host file but you'll need a rooted device in order to edit it. Once that's done, all of the common Tablet OSes have several terminal apps available. Another option would be to use the Android Debug Bridge to edit it. Just copy the host file to the device and use the following command (assuming that the device is at F: and you've put your host file there):
adb push F:\hosts /system/etc/
This will put the host file on the device shared drive over the stock file.
A better tutorial is on howtogeek.com
NOTE: If you have an internal DNS server then you can (and should) just add an 'A' record for it instead.