It started with words associated with printing and impressions. Be it engraving or embossing, offset, foil stamping, or die-cutting, we are referring to impressions on paper. The core business for this company revolves around stationery and therefore refers also to first impressions made by presenting a business card, or receiving a first letter.
From there it was a short step to the name "Impress", because it implied both kinds of impressions and contains the word "press". However, "Impress" was already taken. The next best name was mPress, still making it possible to play games with the letter "i" in front of the logo.when desired. It also implies the word empress, a female emperor, which wasn't all wrong either, since Maggie Schneiderman was most likely to inherit the business eventually. Of course the "m" also stands for the em space, a typographic measurement (the width of the "lower case letter "m" in any given typeface).
The task then was to convey all that visually and create a unique and playful logo which could reproduce in a variety of sizes and printing techniques.