If an aircraft has undergone an approved STC, such as conversion to taildragger configuration from tri-gear, the original model registration is not normally changed to reflect the effect of the mod. There are an awful lot of Piper Tri-Pacers that have been converted to the Clipper/Pacer configuration, for example, and they still show Tri-Pacer registrations. When the Cessna 150 was introduced, there were plenty of howls as to why did one have to carry around an extra 40 pounds? The Texas Taildragger STC is a taildragger mod of the Cessna 150.
Keeping the original registration simplifies tracing of applicability of ADs, for example, which are mandatory and wards off a lot of paperwork snafus and grief. And, where would you draw the line in changing the registration-based on the extent of the mod, or what? Keep the original simplifies aircraft records with a logbook entry of the STC installation. Would you want to pay the cost of re-registration? Probably not since Bill Clinton put Federal agencies on cost collection for all services rendered.