Ahh, that's a harder problem... But I think the best route is to stay with openness and honesty. Let each partner decide what's "too much" information, both in terms of what they hear about other partners, as well as what you share about them. Discuss it with each person and do what seems right by everyone. Err on the side of not sharing things that people would rather be kept private.
I caution against pretending to be monogamous, or telling them what you think they want to hear. It might seem convenient on the surface, and it will work for a little while, but eventually it will explode in your face. Your partners are (presumably) grown-ups. They can deal with information, though it might take some time. But they can't react to what they don't know.
I am who I am. I don't need labels to define me. They're sticky, and I hate the glue they leave behind.