No. You can't.

Database connections are tightly connected with Users. You need to create multiple connections with different different username and passwords. I can feel your pain but it is not possible. I am also using multiple databases for multiple applications and environments within single database server. For security purpose staging and production users are different and app users are also different.

Short way is: Use can create new user who have access of all those Databases but it is not recommended for all team members.