It is better to pick names with actual words. An attacker can otherwise say that the answer is just a bunch of random characters, and there is a risk that a naïve customer support representative may accept it.

In order to deploy this successfully, the attacker would have to know that you used a random string...how would they know this without having access to the string itself?

Not necessarily - they're given multiple "tries" so they can just pick "a bunch of random letters" as one of their first few choices in hopes that they guessed correctly.

Ugh...

Mine was "78 nails and 7 Greek philosophers", which works a little better on the phone. ;-)

That's really the best use for security questions: have fun with customer support.

"Pet's name?"

"ICUP."

"Can you ........ Oh."