The solution to change the country/region setup was accepted by my client, so I will go with this option.
I haven't test the subscription to the event in the code unit, so I can't talk about this solution, but I guess it would have been the way to go if my client didn't want to change the position of the contact.
For the others solutions about removing the field in the layout: it doesn't work. Because the way this array of address is build, if the country/region is setup to have the contact name "after company name", this field will show the contact name OR the first line of address if the contact is empty. Removing the field, means that the the first line of address won't show if the contact is empty...
Thanks!