Effect of Changing the Plan Name when Insurance Vendor Changed

Summary

We have insurance plan where current vendor is A. But this year the Insurance Vendor changed and it is vendor B. All the coverages are same.

Content

We have insurance plan where current vendor is A. But this year the Insurance Vendor changed and it is vendor B. All the coverages are same. In this case, if we rename the plan name from Insurance Plan A to Insurance Plan B wll there be an impact for past records or how could be the effect ?

Any ideas on this ?