The element of murder means this transformation is happening because of some measure of choice.
The serial killer that lives inside your psyche is a beneficial archetype that, though it lives in the shadow, is ultimately a part of your long-range growth and expansion. Such an image might be very frightening in a dream, but it must be examined through the lens of the universal principles it is expressing. [1]
If you are the killer in your dream, this means you will be involved in some dishonorable adventure which will damage your reputation.
If you were killed or pursued by the serial killer, this symbolizes enemies who are working against you.
If you dream that the killer spares your life, you are hopeful that an enemy or rival will stop working against you in real life. Be careful about relying on hopes, however! [2]