Is this alien "Enki" in anyway related to "Comet Encke"? Is it just me that thinks they sound alike?

Not directly related. It was named after the person who identified it as a periodic comet. [link to en.wikipedia.org]

The question remains of who Enke was named after. Enki or Enke seem to be somewhat popular names in Europe at least, I've seen several others with these as first or last names.

NASA seems to have a thing for naming stuff after Sumerian gods. For example, their solar wind program is called ENLIL. And the Interstellar Boundary Explorer (IBEX) is named after one of Enki's totem animals. Other examples exist, seek and ye shall find.