It was expected and finally Google has introduced vanity URLs for Google+ Plus profiles. Now one can customize and change long Google+ profile URL into small easy to share URL. As with other Google+ features, option to customize profile URL will be slow off the block due to limited availability. As of now, vanity URL feature will not available to everyone. Only selected few “verified” profiles and pages can use this feature for custom Google+ profile URL.
Format of vanity Google+ Plus URLs
Being Google+, it has added “+” sign even to short profile URLs. Hence, expected short URL like google.com/hugoboss is infact in google.com/+hugoboss format.
Many short URLs of famous brands and celebrities are already live – for example: google.com/+davidbeckham, google.com/+hughjackman, google.com/+toyota, google.com/+britneyspears and more. [source]
How to get custom vanity Google+ Plus profile URL
It will be difficult to get custom Google+ URL, as this feature limited to verified profiles and pages. Hence, first step is the make sure your profile or page is verified. You can send verification request using this form for verified badge to your Google+ page.
Once you are verified, chances of getting vanity URL increases. As Google opens up this feature to more users, “verified” user are first to receive this feature bump. Further, it is expected – Google will expand this feature to every user. Google has made process of using this simple feature into a complicated routine, when compared to quick and easy vanity URL feature provided by Facebook and Twitter.
Thanks for the info, I have filled the Google+ page verification request