I see that Google and Blogger and maybe other have a customized Google Plus URL.
Google is only beginning to roll out these vanity URLs. Currently, only a few thousand verified and well known people and brands have it, although they will be adding more over time. See this post for (not much) more information.
In the meantime, you should be able to create a redirect from your own website to your profile. (It may be argued that this is a better solution, even.) You can also setup a Google+ Badge to let visitors to your website go to your profile or follow you directly from your site.
Google+ is now rolling out vanity URLs, provided you meet the eligibility requirements
Before you can get a custom URL, your account needs to be in good standing and meet the following requirements:
Eligibility for People:
- 10 or more followers
- Your account is 30 days old or more
- A profile photo
Eligibility for Local Google+ pages: Must be a verified local business
- Eligibility for Non-local Google+ pages: Must be linked to a website
Getting your custom URL through Google+
If you meet the above criteria, you'll see a notification at the top of your Google+ page or Profile.
- Click on the Get a custom URL button to get started.
- Alternatively, from the "About" tab on your Profile, click on the "Claim" link located under your Google+ URL.
- You'll see the URL for which you're approved. You may see more than one option. In this case, select the one that you like best. You may also be asked to add a few numbers or letters to make the custom URL unique to you.
- Tick the box to agree to the Terms of Service.
- Click on Change URL.
- You may be asked to verify your account by mobile phone number. A box will pop up asking you to do so. If you have a verified phone number, skip to step 6. a. Enter your mobile phone number. b. Tick the box to make it easier for people who have your phone number to find you on Google services. c. Check your phone for the code that was sent to you. d. Enter that code in the box. e. Click on Verify.
- Once approved, this URL will be linked to your Google+ page or Profile, so make sure that everything is exactly the way you want it. Once your URL has been approved, you can't request to change it. When you're sure, click on Confirm.