This KB illustrates that how to get server and database names from SSAS.
The procedure to get the Server Name and Database Name from the SQL Server Analysis Services is as follows:
Open the SQL Server Management Studio with the server type as the Analysis Services.
In the Object Explorer window, right click the database to get the server and database names, and click Properties.
Figure 1: Object Explorer window
In the property window, you can get the Database name from the Name field and Server name from the Server field. This is illustrated in the following screenshot.
Figure 2: Property window
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