Select Table_2.Date, MAX(t1analyst.Name ), MAX( t1j.Name ), MAX(t1acct.Name )
From Table_2
left join Table_1 t1analyst on Table_2.Analyst_EID = t1analyst.EID
left join Table_1 t1j on Table_2.Journey_EID = t1j.EID
left join Table_1 t1acct on Table_2.Accountant_EID = t1acct.EID
group by Table_2.Date
Order by Table_2.Date ASC

DECLARE @Table1 TABLE (
    EID INT,
    EmployeeName VARCHAR(32),
    Title VARCHAR(32),
    Number CHAR(12)
);

DECLARE @Table2 TABLE (
    EmpDate DATE,
    AnalystEID INT NULL,
    JourneyEID INT NULL,
    AccountantEID INT NULL
);

INSERT INTO @Table1
        ( EID, EmployeeName, Title, Number )
VALUES  ( 1, -- EID - int
          'John', -- EmployeeName - varchar(32)
          'Analyst', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          ),
        ( 2, -- EID - int
          'Sam', -- EmployeeName - varchar(32)
          'Journey Man', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          ),
        ( 3, -- EID - int
          'Sandra', -- EmployeeName - varchar(32)
          'Accountant', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          );

INSERT INTO @Table2
        ( EmpDate ,
          AnalystEID ,
          JourneyEID ,
          AccountantEID
        )
VALUES  ( '2012-02-01' , -- EmpDate - date
          1 , -- AnalystEID - int
          2 , -- JourneyEID - int
          3  -- AccountantEID - int
        ),
        ( '2012-02-03' , -- EmpDate - date
          NULL , -- AnalystEID - int
          2 , -- JourneyEID - int
          NULL  -- AccountantEID - int
        ),
        ( '2012-02-04' , -- EmpDate - date
          NULL , -- AnalystEID - int
          NULL , -- JourneyEID - int
          3  -- AccountantEID - int
        ),
        ( '2012-02-05' , -- EmpDate - date
          1 , -- AnalystEID - int
          2 , -- JourneyEID - int
          3  -- AccountantEID - int
        );

SELECT * FROM @Table1;
SELECT * FROM @Table2;

SELECT
    *
FROM
    @Table2 t2
    OUTER APPLY (SELECT t1.EmployeeName FROM @Table1 t1 WHERE t1.EID = t2.AnalystEID)dt1(AnalystName)
    OUTER APPLY (SELECT t1.EmployeeName FROM @Table1 t1 WHERE t1.EID = t2.JourneyEID)dt2(JourneyName)
    OUTER APPLY (SELECT t1.EmployeeName FROM @Table1 t1 WHERE t1.EID = t2.AccountantEID)dt3(AccountantName);

use tempdb
go

CREATE TABLE Table_1  (
    EID INT,
    Name  VARCHAR(32),
    Title VARCHAR(32),
    Number CHAR(12)
);

CREATE TABLE Table_2  (
    Date  DATE,
    Analyst_EID  INT NULL,
    Journey_EID  INT NULL,
    Accountant_EID INT NULL
);

INSERT INTO Table_1
        ( EID, Name, Title, Number )
VALUES  ( 1, -- EID - int
          'John', -- EmployeeName - varchar(32)
          'Analyst', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          ),
        ( 2, -- EID - int
          'Sam', -- EmployeeName - varchar(32)
          'Journey Man', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          ),
        ( 3, -- EID - int
          'Sandra', -- EmployeeName - varchar(32)
          'Accountant', -- Title - varchar(32)
          'xxx-xxx-xxxx'  -- Number - char(12)
          );

INSERT INTO Table_2
        ( Date  ,
          Analyst_EID ,
          Journey_EID ,
          Accountant_EID
        )
VALUES  ( '2012-02-01' , -- EmpDate - date
          1 , -- AnalystEID - int
          2 , -- JourneyEID - int
          3  -- AccountantEID - int
        ),
        ( '2012-02-03' , -- EmpDate - date
          NULL , -- AnalystEID - int
          2 , -- JourneyEID - int
          NULL  -- AccountantEID - int
        ),
        ( '2012-02-04' , -- EmpDate - date
          NULL , -- AnalystEID - int
          NULL , -- JourneyEID - int
          3  -- AccountantEID - int
        ),
        ( '2012-02-05' , -- EmpDate - date
          1 , -- AnalystEID - int
          2 , -- JourneyEID - int
          3  -- AccountantEID - int
        );

--SELECT * FROM Table_1;
--SELECT * FROM Table_2;

Select Table_2.Date, MAX(t1analyst.Name ), MAX( t1j.Name ), MAX(t1acct.Name )
From Table_2
left join Table_1 t1analyst on Table_2.Analyst_EID = t1analyst.EID
left join Table_1 t1j on Table_2.Journey_EID = t1j.EID
left join Table_1 t1acct on Table_2.Accountant_EID = t1acct.EID
group by Table_2.Date
Order by Table_2.Date ASC


DROP TABLE Table_1;
DROP TABLE Table_2;

--============================================================================================================
--      Create and populate the test tables. This is NOT a part of the solution.
--      I did, however,add the expected PK's which also create indexes.
--============================================================================================================
DECLARE @Table1 TABLE
        (
        EID             INT             NOT NULL PRIMARY KEY CLUSTERED,
        EmployeeName    VARCHAR(32)     NOT NULL,
        Title           VARCHAR(32)     NOT NULL,
        Number          CHAR(12)        NOT NULL
        )
;
DECLARE @Table2 TABLE
        (
        Date            DATETIME        NOT NULL PRIMARY KEY CLUSTERED,
        AnalystEID      INT             NULL,
        JourneyEID      INT             NULL,
        AccountantEID   INT             NULL
        )
;
 INSERT INTO @Table1
        (EID, EmployeeName, Title, Number)
 SELECT 1,'John'  ,'Analyst'    ,'xxx-xxx-xxxx' UNION ALL
 SELECT 2,'Sam'   ,'Journey Man','xxx-xxx-xxxx 'UNION ALL
 SELECT 3,'Sandra','Accountant' ,'xxx-xxx-xxxx'
;
 INSERT INTO @Table2
        (Date, AnalystEID, JourneyEID, AccountantEID)
 SELECT '2012-02-01', 1   , 2   , 3    UNION ALL
 SELECT '2012-02-03', NULL, 2   , NULL UNION ALL
 SELECT '2012-02-04', NULL, NULL, 3    UNION ALL
 SELECT '2012-02-05', 1   , 2   , 3
;
--============================================================================================================
--      Solve the problem only 1 scan of each table.
--============================================================================================================
 SELECT Date           = CONVERT(CHAR(10),t2.Date,101),
        AnalystEID     = MAX(CASE WHEN ca.AttributeName = 'AnalystEID'     THEN t1.EmployeeName ELSE '' END),
        JourneyEID     = MAX(CASE WHEN ca.AttributeName = 'JourneyEID'     THEN t1.EmployeeName ELSE '' END),
        AcccountantEID = MAX(CASE WHEN ca.AttributeName = 'AcccountantEID' THEN t1.EmployeeName ELSE '' END)
   FROM @Table2 t2
  CROSS APPLY (SELECT 'AnalystEID'    ,AnalystEID UNION ALL
               SELECT 'JourneyEID'    ,JourneyEID UNION ALL   
               SELECT 'AcccountantEID',AccountantEID) ca (AttributeName,AttributeValue)
   JOIN @Table1 t1 ON t1.EID = ca.AttributeValue 
  GROUP BY t2.Date
  ORDER BY t2.Date
;