Switch endpoint for OIDC connection

We’re integrating with a subsystem using OIDC. The subsystem is only using the user’s name and email address to perform a match. If we switch to a different IdP, would we have any issues if the user’s name and email address stay the same? Ie.

From: IdP 1 ----> auth0 -----> subsystem
To: IdP 2 -----> auth0 ----> subsystem

Thank you.