Am I overreacting to my boyfriend's sensitiveness at work?

We’re both on the same team. My boyfriend and I have been dating for 6 months now. Our relationship is a secret thus far, a few knew.
However, there’s this girl he works directly with who doesn’t know about us yet. It somewhat bothers me because of how close they are on a daily basis. They are probably together more than he is spending time with me. I am not the jealousy type, but I don’t understand why he refuses to tell her about us. And in particular, her. I spoke with him several on occassions about this, but his reason behind not telling her was the awkwardness. Am i overreacting for being upset with him for refusing to tell her about us? I need a second opinion. I understand work/personal issues, but he won’t admit he likes her (he denied this every time I brought it up). Should I trust him on this? Should I let it go?
i need a second opinion – men and women are welcome