UPDATE Clients AS T1

 INNER JOIN

(SELECT DISTINCT
Clients.ID_Client AS FED,
Clients.Name,
SecondTable.Client_Name,
SecondTable.ABI_Code AS ABI

FROM  SecondTable INNER JOIN Clients ON SecondTable.FieldToUpdate=Clients.Name) AS T2

SET T1.FieldToUpdate = T2.FED
where T1.ABI_Code =T2. ABI