What is the name of this fruit?
This is a passionfruit. It comes from a plant whose scientific name is Passiflora edulis.



It's indeed a climber, as you can see:



Finally, a curiosity about the name passion fruit. The fruit is called passion fruit because the flower is called passion flower. This is the flower: 



But why it is called passion flower? Passion here has nothing to do with sexual love or desire, the common meaning of "passion", but with the suffering of Jesus. 

Some say that it's because the flower resembles (?) the crown of thorns placed in Jesus' head. Other say that it symbolises Jesus' wounds. In fact, in portuguese we call it "flor das cinco chagas", or flower of the five wounds.

EDIT: thanks to @AlanBoyd's comment, you can see that its connections with Christianity are way more complex: https://en.wikipedia.org/wiki/Passiflora#Etymology_and_names 



Post Scriptum (not related to the question): this plant is native to Brazil, and I had a couple of specimens in my yard. One of the most interesting things about passionfruits in Brazil is that it attracts an insect that we call "percevejo do maracujá", or passionfruit bug in a very free translation. Its scientific name is Diactor bilineatus, and it's one of the most beautiful insects to me. I loved to see them feeding on my passionfruits. This is the adult on a passionfruit (where you normally find them), and the nymph is even more colourful: