Ray passing through point B on line ACB can be named as ray BB'.

Explanation:

1. Understanding rays:
In geometry, a ray is a part of a line that has one endpoint and extends infinitely in one direction. It can be thought of as a straight path that starts from a point and continues indefinitely in a particular direction.

2. Identifying point B on line ACB:
To name the ray passing through point B on line ACB, we first need to locate point B on line ACB. Given that B lies on line ACB, it means that B is a point on the line segment AC.

3. Naming the ray:
Once we have identified point B on line ACB, we can name the ray passing through B. Let's name it BB'.

4. Visual representation:
To visually represent the ray BB', we can draw a line segment with an arrowhead on one end starting from point B and extending infinitely in one direction. This arrowhead indicates that the ray continues infinitely in that direction.

5. Importance of naming rays:
Naming rays is important in geometry as it helps us identify and refer to specific rays when discussing properties, angles, and relationships between different geometric figures. By naming the ray BB', we can easily refer to it in future discussions or calculations.

Summary:
In summary, the ray passing through point B on line ACB can be named as ray BB'. It is a part of line ACB that starts from point B and extends infinitely in one direction. Naming rays is essential in geometry for easy reference and communication when discussing geometric figures and their properties.