It's a completely necessary adaptation to deal with both dangerously pedantic fairies and the douchebag end of humanity. They have to defend against both those that abuse The Laws and those that disregard it entirely.
The horn and hooves and teeth mostly deal with the latter- once one forgoes the sanctity of The Laws in favor of profane behavior in front of a Holy Beast, you are nothing more than troublesome meat.
Those that play games with The Laws require more inventive solutions though.
It's actually very nearly impossible for most beings to keep their True Names a secret. Part of Name Law is that any nickname, title, or Nom De Plume contain at least some element of the True Name. Being that True Names can be used to inflict some particularly foul forms of bondage on them, and unicorns being particularly desirable servants, they've gotten very inventive with discouraging anything from finding or using their True Names. Several strategies are at play in the examples above.
One of the first lines of defense a unicorn lays down is choosing a True Name that is wildly impractical to evoke. Names that are a long string of random numbers was a popular choice for a while until devices that abbreviated the name as an equation while retaining its vaildity became available. Others chose things that aren't easily expressed verbally, like extremely specific colors, or pieces of music. Incarnadine chose an extremely specific shade of red, but now that hex codes are a thing, she's taking steps to obscure and possibly shift the meaning of her true name away from something that can be expressed in six characters and a hashtag.
Others chose pieces of music, where you'd have to write out the sheet music or play the whole damn song every time someone wanted to use the name, which can then be obscured by nicknaming yourself after the band that made the specific recording you are using as a name. Santana has done this, and cleverly chosen a song that everyone forgot the band ever recorded. She's been slowly deleting all records of it off the Internet and acquiring the physical copies of the recording. It's very likely that in the next ten years, it will be literally impossible to find her name in the wild.
Old Nick has put several layers of obfuscation on top of his already wildly-inconvenient-to-invoke name, by choosing a sound that sometimes exists under very specific conditions, nicknaming himself after one of those conditions, and then after a cultural phenomenon that is associated with that condition, and now using a nickname associated with that phenomenon. Anyone who wants to invoke him is has their work cut out for them.
Wolfgang and Pip have done similar levels of obfuscation around their names, with Pip picking a name that has a very specific thing and then going by a synonym for the name of said thing that has like, fifty possible meanings, and Wolfgang running her name through 69 languages on Google translate to get something that is, VERY TECHNICALLY, a translation of her True Name.
Diane picked his name on the basis that anyone trying to invoke the true name of a unicorn will be familiar with how unicorns discourage the practice, and never guess that one is using an actual name. Furthermore, there's an awful lot of Dianes in the world, and fewer still will guess they even need his last name too until they summon a random Diane instead and now have to deal with HER.
Anaphylaxis is going on the offensive by picking a name that, if you even slightly screw up the grammar of the invocation, will summon the lethal medical phenomenon instead :)