This request has been made multiple times before.
While it is sad, the answer is a simple no.
The current images and sprites are static, and do not consist of editable elements which can be changed on the fly.
A single image can take between half an hour to and hour to generate and edit. Adding customisations would require multiple variations of a single image to be created. Not accounting for sprites which take longer and all the additional code required and bugs it could introduce.
Only chance of this happening is if Starmaker does well commercially with enough exposure to warrant a spin off after the Steam release, which would be built from the ground up with this feature in mind.
Note - It is also important to keep in mind Starmaker Story is a side project and most of the developers attention is mainly focused on Roundscape Ecplise