Neo4j doesn't really have a direct equivalent to multiple databases stored within the same server instance. There are three options for achieving this:
1) the closest match would be create run an additional instance of neo4j on the same server. You will need to edit the neo4j.conf file to give the new instance a new port number and a new data directory. This will give you isolation between the data and user accounts in the two databases. The downside is you will need to divide up the RAM on the box before running, effectively limiting both instances to half the RAM.
2) You can attach labels to your nodes to identify which bucket of data (database in the RDBMS world) each node belongs to. You can operate as if the two are isolated even though they really live in the same database instance. Neo4j won't do a lot to help you enforce this, you will need to do the work at the application level. There is a mechanism for you to restrict users to only being able interact with a subset of your graph but you have to write custom procedures and restrict the users to only using those. I haven't tried it but it sounds tedious.
https://neo4j.com/docs/operations-manual/current/security/authentication-authorization/subgraph-access-control/
3) If you are running on VMs or the cloud, you mind as well just create a new instance for your second database. It achieves the same effect as number one but with better isolation of resources.