The only reason it sometimes got called the guavaberry or Chilean guava is because it has a somewhat more perfumed flavour than the blueberry, rather than any particular relationship to the guava. As it happens, guava is, like blueberries, eucalyptuses and cloves and bottlebrushes, in that very diverse family the Myrtaceae, but one wouldn't usually think it worth mentioning that blueberries are related to the guava. It was until recently classified as Myrtus ugni and is much more closely related to the blueberry than to the guava. The Chileans themselves call it murta, which in Spain would refer to common myrtle.

You are very lucky, and perhaps also clever, to have them. They are very delicious. I've only ever eaten them in Chile. I tried growing them here in the Chilterns but despite my pouring lots of collected rainwater on them, they never produced and eventually died.