Pass a table name as a parameter to a stored procedure
Unfortunately, you can't use a variable containing the table name in an INSERT statement. The error message is actually occurring because it is expecting a variable that is a table type to insert rows into, but you're passing a variable with a string value.
You can use Dynamic SQL to execute the command using a variable table name value like this:
CREATE PROCEDURE [usp_SaveToErrorLog]
    @tblName as nvarchar(50),
    @subject as nvarchar(30)
AS
BEGIN
    -- SET NOCOUNT ON added to prevent extra result sets from
    -- interfering with SELECT statements.
    SET NOCOUNT ON;

    DECLARE @Sql NVARCHAR(MAX)

    -- Insert statements for procedure here
    IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(@tblName))
        Begin
            SET @Sql = 'Insert Into ' + @tblName + '
            (ErrorNumber, ErrorMessage, ErrorProcedure, ErrorState, ErrorSeverity, ErrorLine)
            Select
                ERROR_NUMBER(), ERROR_MESSAGE(), ERROR_PROCEDURE(), ERROR_STATE(), ERROR_SEVERITY(), ERROR_LINE()'

            EXEC sp_executesql @Sql
        End
END

What this does is dynamically create your T-SQL command and store it in the @Sql variable. The stored procedure sp_executesql is then used to execute the T-SQL commands in the @Sql variable, which has the actual table name from the @tblName variable.