Question

Does an angle need to be written as Angle ABC or can it be written as Angle B?

Answer 1

<ABC and <B both refers to the same angle. Both ways of writing is correct.

Answer 2

Yes, angle  is made two line ....
A is one point on one  line. C is one point on another line.
If A or C not existed , Angle B  is not defined. 
then ' Angle B '  is the premise 'Angle ABC'