Then "Casa Benvenuti", but IMHO it sounds too much like "Benvenuti's Home"

you can call it "Benvenuti...a casa mia":) 

Are you American? 

Thanks guys!

How does "Casa della Pace" sounds?

Or "Tra mare e monti" because the house is situated between the sea and the mountains?

Opinions and suggestions for a good house name are more thenn welcome.

"Benvenut*!" is a greating that is usually said when one or more guests arrive. It means "welcome" (literarily "well comen"). If the guest is a female you say "Benvenuta!", if he is a male "Benvenuto!", if they are two or more females "Benvenute!" and if they are two or more people, male or mixed gender, "Benvenuti!". "Benvenuto" is also an, a bit out of date, first name and "Benvenuti" is an Italian surname.
 

People should feel welcome when they come to this house.

Do you (or anybody else of course) have other suggestions for a house name?

Feel free to comment....