The icon represents not only the 'C' in Carroll but takes the form of a 3d box, an iconic symbol of design* itself.
The rounded corners on the outside of the box relate to the fine cut finish that sign* companies are expected to deliver.
The icon uses colour reference to CMYK as in print* (purple is an overlap of cyan and magenta).
Overall the logotype works beautifully with the name 'Carroll', it is playful at the same time as being professional and highly recognisable.
Design elements for the brand can be created with the 'C' / box icon and meaningful colours.