SELECT
    name, email, COUNT(*)
FROM
    users
GROUP BY
    name, email
HAVING 
    COUNT(*) > 1

Simply group on both of the columns.

Note: the older ANSI standard is to have all non-aggregated columns in the GROUP BY but this has changed with the idea of "functional dependency":

In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, functional dependency is a constraint that describes the relationship between attributes in a relation.

Support is not consistent: