Dispite the many hours (days, months,?) I've spent happily researching the history of this machine, its inventor and its times, I've discovered almost NOTHING about how the trademark actually came into being. However, analysis of some early documents does closely pinpoint the "when" of its first use.
In Turck's "Origin of Modern Calculator Machines", we are presented with several testimonial letters from early "beta" sites. In two letters, dated in the final quarter of 1887, Felt's invention is referred to only as "the machine" or "the adding machine". In late 1888, letters (from the two Chicago Gas Light companies) specifically mention the "Comptometer" as such. Clearly, the trademark was decided on and, quite possibly issued sometime between these dates.
Betcha cant say it fives times fast...