Yes, the letter that indicates the point which is the VERTEX of the angle MUST
be in the middle.  But it doesn't matter if the two points other than the
vertex are reversed.

Here is why:



The angle with the red arc can be notated as 

angle ADE, ADB, EDA, or BDA

The notation for the angle with the red arc MUST have its vertex D
in the middle. 

The angle with the green arc can be notated as

angle, DAE, DAC, EAD, or CAD

The notation for the angle with the green arc must have its vertex A
in the middle.

ADE and DAE use the same letters in a different order, but they represent
different angles because the letter in the middle which represents the vertex
are different.
 
Edwin