What do you call a person who incurs expenses? Is there a specific word in English?
I think the word you may be looking for is,
- a person who spends, especially one who habitually spends excessively or lavishly; spendthrift.
One possibility is that you're going for "creditor"/"obligee" -- who pays for something on your behalf and whom you now owe (you're the "debtor"/obligor"). This could be, for example, your credit card company, or "Joe, buy me those M&Ms and I'll pay you back". Not sure if this is the sense you mean.
The right word I was looking for is:
expender - someone who spends money to purchase goods or services (Click here for reference)
You could refer to such a person as a *backer" - * i.e., it is their money that is being spent.
Colloquially, there is also the expression "Sugar Daddy" (or "Mama) for an older person who takes on all the expenses of a younger lover. This can also sometimes be used figuratively (although it's kind of disrespectful) in business.