When we are talking about a plane we usually talk about two dimensional surface.But in the real world there is no two dimensional thing.
For example consider a rectangular piece of paper,it has length and breadth but it has thickness which we consider as negligible.
Similarly faces of cube or cuboid forms a two dimensional plane.
When we say this is a plane we say that this is a flat surface.Word sheet is a plane.
Now coming to your question why when naming a plane we cannot use three collinear points?
The reason being that to determine whether it is a plane or not we take two points on that surface. If the line joining that two points completely lies on that surface we say that it is a plane.
Now to draw a unique line we need only two points, So taking three collinear points and then showing it is a plane is worthless.
As i have written plane is a two dimensional surface and line is of single dimension.
So,Likewise on a line there are infinite number of points, on a plane there are infinite number of lines and to determine a unique line we need only two points, so taking three collinear points on a plane through which only one line passes is out of consideration we just need only two points.