Google Plus – How Interactive Emails Work

If your profile is suspended, you will not be able to make full use of Google services that require an active profile such as Google+, Reader and Picasa. This will not prevent you from using other Google services, like Gmail. Your profile can be restored by editing your name and submitting an appeal that will be reviewed by our team, as directed by on-screen instructions.

Here's the official Google policy on names in Google+. (Actually, it is, by extension, their new Google Profile policy, as you can't have one without the other.)

Basically, you need to use your name as you are commonly known. My first name is "Albert" but nobody calls me that, so I use "Al".

Their rules:

• Your common first and last name in a single language script. Leave of the "Dr." and ".jr" and use one language
• Nicknames and pseudonyms need to go in the "other names" field
• No unusual characters (★, @, etc.)
• Your name must represent one individual. Entities should use the Page feature
• Don't use someone else's name
• Names can be changed only once every 30 days

Get all the details at their official policy.

There are two possibilities here:

1. It is a fake e-mail from someone trying to look like Google. We would be able to confirm whether it's genuine or fake if you give us the whole header of the e-mail.

2. It is a genuine e-mail from Google, Someone tried to connect their Hotmail account to your Gmail account using some application (may be a WebApp or a Smartphone App) but failed to do so as he did not have your password. Even here, you have nothing to worry about. Anyhow, to be in the safe side, you can consider that someone whats to gain asses over your account(s) and change your password(s), Security Question and other Security settings.