In v. 4 (release Feb. 2020) of the professional version of Neo4j, it's easy to create new databases. Documentation
In the community edition, it takes a hack:
1. Edit the file NEO4J_HOME\conf\neo4j.conf
2. Un-comment the line: dbms.default_database=neo4j
3. Change the neo4j to whatever database name you want for a new database. Note: names must have between 3 and 63 characters. For example: dbms.default_database=mydatabase
4. Save the file
5. (If applicable) Kill the database server, and close the browser window with the Neo4j UI
6. Start the neo4j server, and open a new browser window, pointed as usual to http://localhost:7474/
7. Both the old (default) database, "neo4j" and the one you just created will show up. However, attempting to switch between them causes an error. If a switch is desired, repeat the above steps starting from (3)
Note: the above steps will create a folder named mydatabase
(or whatever name you used), in NEO4J_HOME\data\databases , and it will populate its contents.
I personally think that switching between databases is such a BASIC operation that Neo4j ought to make it easily accessible in the Community edition!