[kwhitefoot]

If your grandmother is alive and has one dog and you use that dog's name as the answer you are not terribly secure because this information is easy to obtain. It's only virtue is that it is, supposedly, easier for you to remember.

[peterjlee]

I'd argue this is one of the more secure questions compared to other common questions like "Your mother's maiden name" or "The make of your first car".

[OJFord]

Exactly. I don't know how to go about finding out someone's (not personally known to me) grandmother's dog's name, but if I know someone's name then mother's maiden name is easy in the UK.