Updating a table by referencing another table

I have a table CustPurchase (name, purchase) and another table CustID (id, name).

I altered the CustPurchase table to have an id field. Now, I want to populate this newly created field by referencing the customer ids from the CustID table, using:

UPDATE CustPurchase
   SET CustPurchase.id = CustID.id 
 WHERE CustPurchase.name = CustID.name;

I keep getting syntax errors!