The name switch will come into operation at the beginning of April.
The Deeping St James shop will still trade as Terry Wright Cycles, it's the business services division, which includes the insurance replacement operation, that will be restyled.
Nick Ash, TWC's general manager, said:
"Through a programme of continuous investment and with a focus on valuing all of our customers as individuals our business has evolved from its beginnings as a two room cycle shop in Deeping St James to a position where we are one of the UK's largest retailers of bicycles. Our trading style has been under review for over a year and we feel that it is an excellent time for us to make the change."
Charles Ashwell, TWC's business development manager, said:
"We deal with a large number of corporate customers, and are actively seeking new business in this sector. When combined with our operational infrastructure the new brand gives a whole new impetus to our growth initiative and will lead to greater acceptance in the wider business community."
27 staff will transfer to the new company.