How can I change my reference library?

You cannot change your reference library. You should therefore ask the subscription library to disable and delete the account to make a new registration at a new library with a new account.
As there is no library change procedure in NILDE, in the case of users with IDEM-GARR institutional credentials it is necessary to follow this procedure:
1) the user requests the disabling and deletion of his account to his NILDE library
2) the library must verify to don't have outstanding requests with this user (in case, the requests should be closed). At this point the library can proceed to disable and delete the user (deletion is essential)
3) la biblioteca informa l'utente che, ad avvenuta eliminazione, potrà effettuare una nuova registrazione a NILDE andando a scegliere l'altra bibliotecathe library informs the user that, after deletion, he can make a new registration to NILDE going to choose the other library (obviously the user can always use his IDEM-GARR institutional credentials precisely because the library has ordered the cancellation of user account)