I have a dynamic IP, but in practice it seems to change only a few times a year, so I find the monster ID useful as well. The Monster ID is mainly a protection against phishing sites, so if the image changes unexpectedly, you should make absolutely sure that you have the correct Kraken url. Usually if the url is correct, then the different image is due to a change on your end and you should investigate on your end if it's unexpected.
However, in this case I believe the different image is due to a change on our end, probably related to a major update we did in preparation for our launch in Japan. My monster ID changed and I've confirmed that it isn't due to a change in my IP. I'll check with the developers, but I see no reason for concern here (though it's good to be cautious and ask about it).