Which country started the tradition of naming aircraft?
I think the answer has to be that it has always been a tradition.

Since time immemorial - in the most ancient of mythologies and legends, across a very wide range of cultures (in fact I'm not aware of a culture that didn't name water-going vessels - boats of all sizes have been given names.

I don't think it's possible to say which country, or even which culture, started the practice of naming boats.

Many if not most of the traditions, names, roles and structures in aviation were inherited from navigation (including the term navigation of course).

Aviation, in many senses, is simply navigation translated to the sky.
Given this, it would be pretty remarkable if it hadn't always been a tradition to bestow names upon vessels in aviation too.

The Wright brothers' first powered aircraft was named (Flyer, I guess they were too busy pioneering to expend much energy on naming), but really,  it goes back longer than that, to navigation.

What I think is interesting is that now not all aircraft are named, whereas just about every boat that can be painted on still has a name painted on it.