I have a question regarding event sourcing in a microservice architecture.

Suppose that every service stores its own events in a own eventstore, how can i rebuild a read model if the projection needs data from more than one service?

For example we have the UserService and an InvoiceService.
In the invoice service model I work only with the user id, but in the read model I need also the user name for easier queryings.

I thank i have now these options:

1. Store also the user name in the invoice service. Not so good, i think because my source of truth should be still the user service.
2. Create a (rest?) api to fetch the user name from the user service in case of a read model rebuild.

Did I miss something? Does someone know a easier solution?