I would not recommend manually creating and managing those separate connections. I don't know the details of your multi-tenant requirements (number of tenants, size of databases, expected number transactions, etc), but I think it would be better to go with something like Mongoose's useDb function. Then Mongoose can handle all the connection pool details.

update

The first direction I would explore is to setup each tenant on a separate node process. There are some interesting benefits to running your tenants in separate node processes. It makes sense from a security standpoint (isolated memory) and from a stability standpoint (one tenant process crash doesn't effect others).

Assuming you're basing the tenancy off of the URL, you would setup a proxy server in front of the actual tenant servers. It's job would be to look at the URL and route to the correct process based on that information. This is a very straightforward node http proxy setup. Each tenant instance could be the exact same code base, but launched with a different config (which tells them what mongo connection string to use).

This means you're able to design your actual application as if it wasn't multi-tenant. Each process only knows about one mongo database, and there is no multi-tenant logic necessary. It also enables you to easily split up traffic later based on load. If you need split up the tenants for performance reasons, you can do it transparently at the proxy level. The DNS can all stay the same, and you can just move the server that the instances are on behind the scenes. You can even have the proxy balance the requests for a tenant between multiple servers.