When you click 'create instance' in Aura, the name displayed in the Aura console does not match the name of the AuraDB Instance displayed in the Neo4j browser.
Let us assume we've clicked 'create instance' and named ours "ajs_demo1"
However, when you log in to the AuraDB Instance using any client (in this case, Neo4j browser), you don't see “ajs_demo1” and instead see neo4j and system databases.
In essence, it would be better to describe what you are doing as actually providing a name for your instance of Aura rather than a database name.
In this instance, two databases only will be created, the default system database and another one to house your data, which is named neo4j (also default).
Additionally, please note that with Aura, it is not possible to create multiple databases to hold your data within the same instance.