Why does the `find` command use a single dash for multicharacter options?

Is there any reason why the find command goes against the convention of using double dashes for multiple character options?

I mean, for example, why

find -name "my_file.*"

rather than

find --name "my_filename.*"

As @muru said:

Those are not options, but tests, and we already have a convention of multi-character test names with single hyphens - the shell's [ / test command's tests.

It's simply history. Don't over-interpret those things; back when those old Unix commands were invented, there were no conventions, at least not anyway as strong as today. Everybody was doing his own thing. It took a long time until all that was settled, and by that time it was so established that there would have been an outcry, and a lot of carefully hand-crafted scripts would have broken, if there would have been a movement to unify those things.