One database listening on two database names
I see two options.


SQL Alias as mentioned in the comment by McNets.  But I am not sure if it will work in your scenario, when it does work it is a great tool.
Use SQL Replication to create a copy of the database DatabaseOne named DatabaseOne_Report on the same sever.  Depending on a few variables, the two versions of the database will be completely in sync to delayed a bit.