What you are asking for here is any record(s) from Table_2 where the Analyst_EID, Journey_EID and Accountant_EID are all the same. What you really want is to create a pivot or crosstab query. I'm sure there are more elegant solutions but something like this would probably work:

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