All the Android devices that you use are registered with play store. You could rename them to differentiate it on the Play Store. To do this, go to https://play.google.com/ and login with your Google account. From the right side, click on the Settings icon and select Settings from the drop down. This will show the list of Android devices you have registered with Google. This also shows information like device maker, model and when it was registered.
From the list click on Edit against the device you would like to rename. Enter the name and then click Update; this will rename your device name. You could also uncheck the other devices from the list so that they won’t be shown when you try to install an app from the play store.
Also select the option – Keep me up to date with news and offers from Google Play to get the latest news from play store.