How can I authenticate mongodb server identity via mongodb shell?
I am trying to deploy a mongodb instance in my environment. I have
  settled a ssl connection so it is possible to authenticate clients
  (using a certificate they enter and agreed root ca by both the server
  and the client). Is there a way to authenticate the server identity
  too? (I could not find any reference to this issue) . I would like to
  use the mongo shell (without any side programming).


As per MongoDB documentation here MongoDB supports the following authentication mechanisms:


SCRAM
(Default)
MongoDB
Challenge and Response (MONGODB-CR) (Deprecated as of MongoDB
3.6)
x.509
Certificate Authentication.


New in version 2.6.

MongoDB supports x.509 certificate authentication for client authentication and internal authentication of the members of replica sets and sharded clusters.

x.509 certificate authentication requires a secure TLS/SSL connection.

Certificate Authority

For production use, your MongoDB deployment should use valid certificates generated and signed by a single certificate authority. You or your organization can generate and maintain an independent certificate authority, or use certificates generated by a third-party TLS/SSL vendor.

Client x.509 Certificates

To authenticate to servers, clients can use x.509 certificates instead of usernames and passwords.

Client Certificate Requirements

The client certificate must have the following properties:


A single Certificate Authority (CA) must issue the certificates for
both the client and the server.
Client certificates must contain the following fields:

keyUsage = digitalSignature
extendedKeyUsage = clientAuth
Each unique MongoDB user must have a unique certificate.
A client x.509 certificate’s subject, which contains the
Distinguished Name (DN), must differ from that of a <a
href="https://docs.mongodb.com/manual/tutorial/configure-x509-member-authentication/#x509-member-certificate" rel="nofollow noreferrer">Member
x.509 Certificate. Specifically, the subjects must differ with
regards to at least one of the following attributes: Organization
(O), the Organizational Unit (OU) or the Domain Component (DC).



  WARNING
  If a client x.509 certificate’s subject has the same O, OU, and DC
  combination as the Member
  x.509 Certificate, the client will be identified as a cluster
  member and granted full permission on the system.


For your further ref here