When a group of people decide to go Dutch on a trip or a visit to the restaurant, one person may take the responsibility of paying all the expenses for the entire group (usually out of his/her own pocket, but they can also collect budget from the participants in advance) so as not to engage each group member in payment processes and save time. After the event, members of the group compensate by paying their share to this person.

What would this person be called?

If it helps, there is a word for this in Persian, 'Madar-e- Kharj' (literally mother of expenses):

"You don't need to pay money now; John is [the group's / the trip's] Madar-e- Kharj. We will all reimburse him later."

The official answer would be treasurer.
From American Heritage:

One who has charge of funds or revenues, especially the chief financial officer of a government, corporation, or association.

That said, general usage is only when this is in an official capacity. So you are the treasurer for a club or society, and there may be an official bank account associated with this.

On a ship or a plane, the word purser could also be used:

The officer in charge of money matters on board a ship or commercial aircraft.

Both treasurer and purser are somewhat official sounding, and would sound playful at best a group of friends paying for a meal through a delegate. In your example, I might just say "John is paying for now and we'll pay him back later" or "John is handling the money/cash, so pass your cash to him".

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Alternatively, as suggested by @ChrisH in the comments, you might say "John is looking after the kitty". A kitty is defined as (Collins via TFD:

any shared fund of money, etc

A kitty, though, is usually decided before the meal/drinks/event. It's usually used as an alternative to buying "rounds" of drinks. Everyone contributes a specific amount up front, so the bill is self-limiting. Left-over (or even negative!) kitty can be shared equally among participants.

The word that springs to mind for me is "treasurer". The definition of treasurer in the Oxford English Dictionary is:

treasurer - A person appointed to administer or manage the financial assets and liabilities of a society, company, local authority, or other body.

Most societies -for example, a University sports club - will have a treasurer that looks after the finances of the group.

However, it may be a little formal for a group of friends going on holiday or going to a restaurant.

The Bank

Within my group of friends, we call this role The bank. It would be easily understood by those who have never used, nor heard, the term in this context.

John, would you be a dear and be the bank for today's lunch? We'll all settle up with you by the end of the day. Thanks!

The term comes from the traditional role of a bank as a primary lender of (other people's) money. With the modern credit-based society, we sometimes lose sight of the fact that a bank is somewhere behind each of our credit cards and accounts.

From Merriam-Webster:

bank

noun (2) 

Definition of bank (Entry 3 of 5) 

1  a : an establishment for the custody, loan, exchange, or issue of money, 

       for the extension of credit, and for facilitating the transmission of funds