The name doesn't ring a bell for anything spirit-related or demonic. However, within branches of Paganism and Shamanism, everything in nature is to believed to have a soul; trees, plants, flowers, etc. For many Pagans, it is considered respectful to ask the Earth for permission to take, cut, or break something of the earth - or whatever you took would not work in your favor.
Perhaps it's the branch's soul or the essence of the branch that is "speaking" to you. Sometimes it's a good thing, others not so much. If it has not caused you any harm or you have not been getting any negative or harmful vibes from it, then you are probably safe with it. If you have, then it is probably best that you return the branch to the woods where you found it.
If you think it's okay to keep it, maybe you can do something useful with it besides just keeping it to collect dust or chopping it up. Craft it into a staff or wand, or carve magickal or spiritual symbols and place it by your door or in your room for protection.
If you are Pagan, or if you're not but have some knowledge of meditation, you can meditate with it. Go into a deep meditation and see if it's soul or essence appears to you. Perhaps you took that specific branch for a reason - maybe it called to you without you knowing it, and within meditation it can give you or show you a message or its purpose as to why it's "speaking" to you.
Blessed Be
Sage
Source: magick-keys.blogspot.com