SQL join table with a dynamic database name

I have a table which contains a employee ID and a database ID code in database DBX0 table 'FirstTable':

The database name is stored in a different table 'databases' like :

So what I'm trying to do is join the first table with a separate table which is stored in the identified database, like

SELECT * from DBX0.dbo.FirstTable a join (SELECT [DB name] from DBX0.dbo.databases where [database ID] = a.[database ID]).dbo.OtherTable

(I don't think this will actually work with a subquery, but this would return the result that I want in theory.)

I have tried dynamic sql with a cursor to iterate through each database and then only return results based on database ID = database ID and Employee ID = Employee ID, but this returns the results in a separate result per database.

Also tried:

Select * from (SELECT * from DBX0.dbo.FirstTable a join '+@dbname+'.dbo.OtherTable on a.employeeid = b.employeeid and a.dbid = b.dbid)

in dynamic sql, but this didn't work either.

Is there any way to get all of the data in one result?