I have integrated Google plus with my android app. Everything is working fine, i am also connected to Google plus but I am not able to get the name of current user logged.>
Check that you generated both of debug and production Client ID by SHA1 keystores. It display in APIs & Auth -> Credentials tab of your project.
Setting up OAuth 2.0 for Android documentation says:
In a terminal, run the Keytool utility to get the SHA1 fingerprint for your digitally signed .apk file's public certificate.
...example for debug-keystore...
Important: When you prepare to release your app to your users, follow these steps again and create a new OAuth 2.0 client ID for your production app. For production apps, use your own private key to sign the production app's .apk file.