Is there a specific word in English for the owner of a pond/pool?

In china, there are many pools/ponds for finishing, I am wondering is there any specific word for the owner of a pond/pool?

The most direct way to express the idea in English is "pondowner" or "pond owner".

In fact, there's a magazine called "Pond Owner Magazine"¹. It's also fairly conclusive that there's a well-known video game character in the popular Zelda series, who exactly meets your description (a person who owns a pond and leases rights to fish in it), who, in English, is known as "The Pond Owner".

I say "fairly conclusive" because this character is almost certainly modeled after the same class of person you're asking about (which occupies a specific niche in Asian society), and Nintendo chose "pond owner" as the clearest translation.

Sidenote: Predictably, within the community of pond owners, these people call themselves "pondies". So if you want refer to them as a class of people, you might say something like "Boy, those pondies sure are a fishy bunch".

¹ There's also a competing magazine known as "Pond Boss", which markets itself to those "own or manage private waters", but it would be a stretch to say "pond boss" is idiomatic English for pond owners; rather, I imagine "Pond Owner Magazine" beat "Pond Boss" to the punch, and the latter needed to come up with an alternative, but short, descriptive, and compelling title for their own publication.

² Interesting side note: the specific right these "pondlords" are leasing out (the right to take benefit from his property while having no claim on the property itself) is termed, in legalese, "profit-à-prendre".

I'm tempted to make a joke revolving wealth, lifestyle and attitude, but I'm not going to do it.

There is no such thing. Generally speaking, owners of an object do not have any word associated to them, because owning something is not a job, so there is no real need to describe them. Jobs describe the involvement of items, but never imply ownership, such as a farmer and barn animals, or blacksmith and furnace.

For those, you simply use noun-owner, such as gun owner or horse owner

The only jobs I can think that implies ownership would be various political jobs such as King/Emperor (which implies ownership of a kingdom/empire) and Sinterklaas, which implies ownership of gifts and exotic deers

Even something like author, which strongly implies ownership of literatures or painter which implies ownership of paintings, may not be true (they could be employed by others and their work owned by their employees)