Learn English – what do you call the person who passes the trophies to the prize giver/presenter

The word to use for people who lose things would depend on why they are suspected of losing them. They might be absent-minded or forgetful as suggested in another answer, but they could also be disorganized, distracted, or preoccupied, for example.

Loser is not valid because here "lose" is always understood in the sense of winning and losing a competition. It can be neutral, to describe the loser of an organized game or prize, or to diminish those not at the top in business or society, or disparagingly to call someone hapless or a failure.

The only time it does not is when making a play on words. For example, the television show The Biggest Loser features teams of obese people who compete to lose the most weight. The biggest "loser" is thus actually the winner of the competition.

There are numerous other examples in which the obvious noun formed from a verb has a different and stronger primary meaning:

waiter > one who waits, as for a late train

waiter > one who waits on tables, as in a restaurant

boxer > one who packages things in boxes

boxer > one who fist-fights for sport

skipper > one who skips instead of walks

skipper > the chief officer of a ship

Perhaps self-absorbed

absorbed in one's own thoughts, activities, or interests

or egocentric

regarding everything only in relation to oneself; self-centered; selfish

or self-centered

concerned solely with one's own desires, needs, or interests

SUPPLEMENT

Also consider self-directed

(of persons) free from external control and constraint in e.g. action and judgment

Note that this term is often applied to someone who does attend to the needs of other but exerts a good deal of independence in doing so.

and autonomous

Not controlled by others or by outside forces; independent