Some Google searching leads me to believe that the codification of seven "demons" (sum. maškim) is not in any ancient sources. Most of the Google results appear to be about Neo-Pagan and Satanistic uses of the concept, most of which appear to be based on Satanistic Simon Necronomicon (1977) and more recently, Maskim Hul - Babylonian Magick by Michael W. Ford (2010).

I have not read either of these works, but based on the published summaries and reviews, both works appear to refer to ancient Mesopotamian myths selectively while claiming that the ancient sources provide more details than they actually do. This is probably in order to create a more complete vision of the religious message the writers are trying to outline. While this is not necessarily at bad thing, the ancient sources do not offer direct support for kind of interpretation.

The concept of the Seven Sages is a well-known motif that appears in several different traditions in the ancient Mediterranean. In Mesopotamia, it is most commonly associated with a group of sages called the Seven (sebettu) or the Sages (akk. Apkallu sum. abgal (wr. nun-me)). These are most likely the seven names you are looking for, and they can be found on the wikipedia page for Apkallu.

Alternatively, the tradition is sometimes confused with the Greek tradition of the Seven Sages, which is a different thing but shares a historiographical link with the same ancient tradition of knowledge coming from the distant past and being codified by seven great thinkers.

"Demons" are usually only referred to indirectly in incantations and ritual texts. They are rarely referred to in mythological texts, and there are no systematic works treating them in ancient cuneiform sources. Lamashtu (Lamaštu) and Puzuzu are the two best known demons. I have never seen their names listed in a list of seven, and I suspect it is a conflation with the tradition of seven sages as I mentioned above. The definitions of demons in cuneiform texts changed quite a bit over the eras of Antiquity so it's difficult to talk about them in more than general terms.

For more information, check out: Jeremy Black and Anthony Green, Gods, Demons, and Symbols of Ancient Mesopotamia (1992). It probably has most of what you are seeking.