When I use dynamic sql and have WHERE clause I prefer to use sp_executesql SP. That way you avoid SQL Injections:

declare @cSecondDb as Varchar(100)
DECLARE @sql nvarchar(200)
declare @Category as Varchar(25);
set @Category = '1009F'
set @cSecondDb = 'SecondSQLDatabase'
SET @sql = 'select * from '+@cSecondDb+'..mytable where Category = @Category'
EXEC sp_executesql @sql, N'@Category varchar(25)', @Category = @Category

>Hi,
>
>I am testing the SQL Select with a name of the database not current.
>This case works:
>

>use [FirstSQLDatabase]
>go
>select * from SecondSQLDatabase..mytable where 1=1
>

>
>Now I want to put the 'SecondSQLDatabase' into a variable. Here is how I do it:
>

>use [FirstSQLDatabase]
>go 
>declare @cSecondDb as Varchar(100)
>set @cSecondDb = 'SecondSQLDatabase'
>select * from @cSecondDb..mytable where 1=1    -- this is the line that causes the syntax error.
>

>
>The above produces syntax error.
>
>What am I missing?
>TIA