You can Login with you Facebook account or Twitter account simply. Or on the another side you can login with your email id.
If you go for Facebook or Twitter login, you need to set your email id and password first.
Then you need to give your name which you need to control in +Google Search Engine . You should prefer to use your first name and last name which you want in Google search.
If you are a Student or Employee, then first prefer to set your +LinkedIn account. See that you Linkedin name and the name which you gave to control is same so it easy to control. It seems this is having Case sensitivity check that also.
Then you can update your headline if you want.(Mostly not preferred by all).
Then here comes integration with Facebook.
Making the Search engine search enable. Change your name officially.
You can also go for others like Google+,Twitter and so on. But more than 3 is for premium users.
And the list goes on.. You share your profile to get noticed. Enjoy sharing.