One issue with IP addresses is that in regions like Western Europe, IP addresses have become a lot more stable. Years ago, an IP address was allocated when you used your dial-in connection, and was assigned to the connection as long as it was live. One technical reason was that there was a scarcity of IPv4 addresses. But nowadays, IP addresses for broadband connections are allocated for much longer time, as ISPs use more fancy allocation mechanisms. You can easily check that if you look up your external address on a site like whatismyip.com, disconnect your home router, and connect it again and re-check your address.
I want to point out is that there are at least three areas where your IP address is easily linked to your real name and identity. One are ISPs which give that data away, like comcast in the US. Another are payment providers, for example paypal, which can easily link your identity – given by your credit card details – with your IP address. For credit card payments, payment providers need to do that, but there is little what would stop them to sell that data.
But I think it is a third way which is actually most pervasive how the IP address you use for browsing can be linked to your real name. Most people use email daily. Now think about google mail – any time you send somebody an email, it could go to a google account, with or without your knowledge. The IP address of the computer you are sending from is in the header of each email. Your actual name is (in the great majority of cases) in the “from” part of the header. So, google only needs to look at the email headers and store the link between IP and names.
Now, if you look up a web site which has a facebook like button, a twitter button or is using google analytics, you are always connecting with the same IP which is associated to the name in your email.