"Sectionals are named after a major city within its area of coverage." (source): FAA Aeronautical Chart Users' Guide on page 9:

EIK is shown on both the Denver and Cheyenne sectional charts. The name of the Sectional Chart where EIK can be found is shown in the FAA Chart Supplement (pertinent excerpts shown below).
There is, for good reason, chart overlap where sectional chart information (cities, airports, etc.) appears on the adjacent sectional chart, although the overlap is only a few miles.
Why EIK, which is closer to the city of Denver than to the city of Cheyenne, but is shown on the FAA Chart Supplement as being on the Cheyenne Sectional Chart, is likely some geographical location naming convention having nothing to do with its proximity to the city of Denver or Cheyenne. As a note, Boulder Muni (BDU), a few miles west of EIK, is also shown on the Chart Supplement as being on the Cheyenne sectional. But, Rocky Mountain Metro (BJC), a few miles south of EIK, is shown on the Chart Supplement as being on the Denver Sectional.


