No. The Bible reveals that God is triune--that the Father is God, the Son is God and the Holy Spirit is God, yet all remain distinct, in some way, from each other. We know that there is a "person-ness"--mind, will, emotions, relation, etc.--to each but all exist somehow as one being.
The same reasoning is why I say Jesus is truly God and truly man, rather than the typical fully God and fully man or 100% God and 100% man. As soon as certain language is used--"100%" or "fully"--it brings problems such as the often used response: how can Jesus be 100% God and 100% man? Should it not be 50/50? Or whatever. The issue gets more confusing and clouded based on the terminology that is used, which is why it is important to use certain words and avoid others.
Similarly, with regards to the Trinity, we can't say each is 1/3 or something of the sort. We don't know, and can't know, the specifics of the union of the three as one, just as we cannot know the specifics of how Jesus can be both truly God and truly man.
But we do know enough from Scripture so that we can choose appropriate terminology to best describe the nature of God and how each "person" relates to the other and to us. The use of "manifestation" immediately confuses the issue with oneness. The use of "entity" can cause confusion with other spirits or "ghosts" and "apparitions," which are commonly referred to as entities and really don't bring to mind the idea of "person-ness." As I stated above, "person" brings to mind all sorts of important things, not the least of which is that we cal be in relationship with, and know and be known by, this triune being we call God.