I've noticed that in many D/s relationships ( especially the Master/slave relationship) collaring plays a big role. The Master or Dominant will present Their submissive with a collar as a symbol of their status as the sub in the relationship. Most of the Masters will actually use it as a symbol of Their slaves ownership. My thought is why can't it be more than that?
To me being collared by Daddy does not mean He owns me, rather that I have given myself to Him. To me there is a big difference. Daddy has told me many times before that just because I have given myself over to Him, I am not property. He does not own me and wouldn't want to. He loves me and just because I have given Him complete control of my life, doesn't mean that He wants me to be His slave. That is not the kind of relationship we have. I know that it is right for some people, but not for us.
I love Daddy and when I am collared I will show it off with pride. To me it is a symbol of my commitment to Him and our relationship. When He places it around my neck, I will never take it off. Only He can do that, and I know He wouldn't do that unless absolutely necessary for our safety and/or comfort. A married woman would not remove her wedding ring to go into public, just like I would not remove my collar. To me it would be more embarrassing to be without it, than it would be to wear it. It shows the outside world that I am proud of being my Daddy's girl and I would never hide that.