Is naming things a fantasy in Japan?
I think you meant to say "fetish" rather than "fantasy"?

Not that I'm aware of, but in many cultures, naming is of great significance, there are often attitudes that being given a name or title is perceived as a great honour. 

Catholics does this, for example, when they receive their baptized name; as well as Buddhists, when they receive their dharma name. 

Many monarchies have a tradition of the monarchs taking on a new regnal name when the new monarch ascended to the throne.

It's also common trope for feudal servants/subordinates serving a new master to take a new name, it's a sign of throwing away their past and therefore subservience to the new master.

Another common trope is a new pet being drawn to feel happy when they're first named. Often the trope goes that the pet feels unhappy/angry/uncomfortable while the owner scrolled through a few names that then got rejected before they ended with the one that the pet seems to respond well to (IRL, this is likely just reflection of the owner being happy for having finally picked a name, because chances are the pet doesn't care or understand).

This is definitely not unique to Isekai genre.