Hrmm.. IAH trip coming up, I think my response will be "Sorry, that's SSI."

TSO: What's your name?
Me: Sorry, that's SSI ?
TSO: Excuse me?
Me: It's SSI, I can't tell you.
TSO: It's printed on your boarding pass right here.
Me: Then when would you be asking me then?

Or better yet, maybe say nothing and when they ask you to say it again, say "I just did". Those letters are silent in my pronunciation.