People working for a company tend to think of that company as their brand. That’s why it’s good to work for a big brand, like Google. You introduce yourself this way: “Hi, I’m John Smith, of Google.” People are like: “Mr. Google, it’s such a thrill to meet you. I’ve heard so much about you!”
Your company is rarely your primary brand, though. Your main brand is you. Don’t forget that, and don’t be ashamed of it. Everybody loves being on a team—especially an all-star one like Google—but think about it this way: People change teams (and jobs) all the time, and you’ll still be you long after you’ve left Google.