When I pull up to a rental in my Lotus and my GC asks me what exactly I "do," I say "I work for the mob."
What kind of question is that, anyway? "What do you do?" I make money. I invest my time into learning how to make more money. Then I take calculated risks that enable me to continue making more money.
Don't get me wrong... I don't care about "money". I care a lot more about TIME than money, and I don't want to be a schmuck that works 300 years for a BOSS, hoping for a pension and a gold watch, only to be fired a week before my gold watch ceremony and hoping Walmart has a spot for me a couple days a week to make up for the pension I didn't get.
Anyway... how transparent should you be? That depends on your situation. If you have the freedom to take calls, do it. If you have to do it on your lunchbreak in order to keep your current boss happy, then do that.
Just remember you currently have a JOB, which stands for "Just Over Broke".
Good luck. :)