You most likely have a more recent mass-produced version of a National Chalk pool cue.
There are a few incarnations of "National" branded pool cues, including ones with logos containing a red circle with a letter N in the middle (though I didn't find any photos of that version).
The first are the cues from "National Billiards Company" of Cincinnati, OH. As far as I know these are not related to the cues from the "National Chalk Company" of Chicago (and later, Gerogia). They made quality queues in the beginning but then brought in some poor quality imports (see images).
The "National Chalk Company" began producing pool cues in Chicago, IL United States in 1968. The original National Chalk Company pool cue manufacturing operations were set up by Richard Helmstetter. Initially, Craig Peterson, Bob Meucci, Ricco Cervantes, and others worked there making pool cues. These cues would be considered generation 1, and are identified by the word "National" being engraved directly into the butt cap.
Near the end of 1969, the National Chalk Company moved to GA, and ended up closing its doors shortly thereafter.
After this, cues were imported by another (unknown company) which carried the National name. Quality was poor, and these cues can be identified by the word "National", similar to above, but on a sticker (see photo) instead of being engraved.