Nobody else has had a go at this so let me see if I can help.
I think you might be able to do it with an "If" statement.
In column 6 on the english sheet you could try =if(d1=greeksheet!c1,greeksheetb1," "). This should look at the value in the fourth column (d) in the english sheet and compare it the third column on the greek sheet (c). If the numbers are the same it should return the value of the greek last name.
If you want Cols 6 & 7 as Greek first and last name, you will need to change the column letters!
Once you have the corrext formula, you will be able to drag ti to all the relevant cells.
It takes longer to type and try and explain than it does to do, but I hope that helps!