Double goose or Double geese?
'double goose' is a specific term that relates to the feather filling in jackets. It is always singular.
Examples:
"My jacket is double goose", or "My jacket has double goose filling", or "I have 2 jackets and they are both double goose."
Double room
A 'double room' is an extra large room.
Examples:
"I booked a double room at the hotel."
If I wanted 2 extra large rooms, I could say "I booked 2 double rooms".
Double chins
A 'double chin' refers to one chin (but it looks like 2 because of the rolls of fat)
Examples:
"That person has a double chin"
"Those two people both have double chins".