Not all blog owners are certain of the relationship between the blog URL, and usefulness of the utilities in Webmaster Tools.
If you're using Webmaster Tools with your blog (and this you really should be doing), you'll notice that the tools, as provided, reference the URL of the blog. If you change the blog URL - either as a simple BlogSpot rename, or when re publishing to a custom domain - you need a new Webmaster Tools entry. And, you'll need to retain the old Webmaster Tools entry.
Unless your readers are immediately observant of any URL change, there will be some readers who continue to reference the blog using the old URL.
This will be especially true for a BlogSpot rename, with the Post Feed Redirect used to forward the old feed URL to the new feed URL. The old feed URL will continue to bring you readers, long after you change the URL of the blog.
The more transparent you make a URL change, the less likely some readers will be to update bookmarks, or BlogList entries. This will cause secondary effects - as when their readers become your readers, and reference your blog using the old URL.
Conversely, some readers will update their bookmarks, and links in their blogs, to point directly to your new URL, immediately upon observing the notice in your stub blog. Their readers, seeing the newly updated links to your blog, may do the same.
Since the various utilities in Webmaster Tools reference the URL used to read your blog, you'll find that both the old and new URLs will show activity. To properly monitor the activity, you'll need to watch the Webmaster Tools utilities for both URLs, for a while, after the URL change.
The bottom line here is that you will need a new Webmaster Tools entry, to equal the newly published URL of your blog, almost immediately. You will also need to retain the old entry for some time, after the URL change.
An Important Update
If you did not use a Blogger / Google account when you Followed this blog, years ago, you are probably not Following now . During the past...