Last month I wrote to the Library of Congress to find out if I needed a new ISSN for Paperback Writer (I've been using the same one I received for my old weblog ten years ago.)
I have gotten a response, and turns out that I did need a new one:
This is your official notification that the following ISSN assignment(s) have been made under the auspices of the U.S. ISSN Center at the Library of Congress. Please print or save this notification for your records.
Please note that a separate ISSN is needed for each medium version (e.g., print, CD-ROM, online) you publish. For your convenience, we have reported the ISSN of all medium versions of this title we have in our database even if not all were assigned at this time.The preferred locations for displaying the ISSN on a printed serial are the upper right-hand corner of the cover, or the masthead, or another prominent place. The ISSN should always be printed with the letters ISSN preceding the number as we have listed it above. The preferred location for display of the ISSN on an online publication is the title screen or home page. If you publish a title in both print and online versions, please print both ISSN together on each version, filling in the blanks in the example below with the digits of your ISSN:
ISSN _ _ _ _- _ _ _ _ (print)
ISSN _ _ _ _- _ _ _ _ (online)
An ISSN remains valid as long as the title remains unchanged. Please inform us in advance of any planned changes in your title so we can determine if a new ISSN is needed.
Attached to the email version of this message are documents about uses and benefits of the ISSN, how to present and title your serial, and your Copyright obligations. Our web site at www.loc.gov/issn includes these documents as well as additional ISSN information and an ISSN application form that you can download for future ISSN requests. If you have any questions or if we may be of additional assistance, please feel free to contact us.
ISSN Publisher Liaison Section staff
So that's the official ruling on whether or not you need a new ISSN if your weblog name and URL changes. If you would like to apply for an ISSN for your blog or online serial publication, here are the links again:
For U.S. bloggers, go to the Library of Congress's U.S. ISSN center to get started (where you can now even apply for an ISSN online.)
If you reside outside the U.S., you can apply to either the national ISSN center in your country or (if your country doesn't have a center) the ISSN International Centre in Paris.