Does renaming a pokemon to its original name count as a nickname?
I'm sorry, but the Pokemon will retain the changed nickname.
So if you have got a Pikachu you called "Pika" earlier, you may visit the house of the name rater and change it it to "Pikachu", but if it evolves it's still called "Pikachu" and not Raichu. (In Camphrier Town right after Lumiose City you will find the Name Rater in the Pokemon Center.)
Furthermore, if you trade it and your friend evolves it to Raichu it's still called "Pikachu" and he will NOT be able to change the name of it.(Due something like "it's the earlier trainers spirit")
So, no you can't delete a pokemons nickname. But you may change it to "Raichu" for example, trade it - and if your friend evolves it later on, the name is matching.
Except for using a cheat-module, this is the only way to deal with stupid nicknames :/
--- Update --- There is the chance of using a bug in generation 6: If the name contains special chars (like the asian ones) the game will remove the nickname if you swap your pokemon with somebody else. This way would cost you about 20 bucks to buy the asian version :/ Which is quite expensive (for a nickname) - but the only way, if you don't want to be reported for an inapropriate name :D
--- Update #2 --- Since I could not find any evidences on the internet, I may just rely on the two user comments below. It may be possible to change a pokemons nickname in the Generation V and VI as bulbapedia noticed the following:
Starting in Pokémon Black and White, whenever a player catches a Pokémon and decides to nickname it right afterwards, he or she may tap the Pokémon's sprite or model on the nickname screen to reset the nickname back to the Pokémon's species name.
This means, one tap and your nickname will be set to the species name. By accepting this nickname the game would check, wether it matches the speciesname or not and would remove the nickname-bit. This would explain, why user2357112 was able to restore it's speciesname.
I do not own these generations by myself, so if anybody could check this, i'd love to credit him here. Thanks in advance.
No. Since Diamond/Pearl there is "Nicknamed" bit stored in individual values bytes, probably to allow dynamically changing the nickname when Pokémon was traded internationally using GTS. The name rater always sets this flag, even if you changed the name to species name.
However, this only applies to Diamond/Pearl, and games released after it. Before GTS that allowed online trades (well, technically Pokémon Communication Center also allowed trading, but it was Japan-only, so no issue here), there wasn't a nickname flag. The game determined if the specie was nicknamed in very simple way - if it had the same name as the specie in your name, it was assumed to be not nicknamed.
This obviously caused a problem when the Pokémon was traded internationally and evolved, but before fourth generation such trades were rare (before you ask, yes, Game Boy games allowed international trades, but only between versions using Latin alphabet).
Just for fun, the only Pokémon that couldn't be restored to original nickname in second generation was Porygon2, because you couldn't type "2" normally.
In fifth generation (not sure about sixth), there is the only way of removing nicknames I'm aware of, but it's probably not intended to be used in this way. There is a filter in a game (client-side, server instantly rejects such names, which is an issue with specie names like Nosepass) that automatically removes a nickname when you try to send to the GTS something with a censored nickname (warning: link contains potentially offensive words). You may want to use something censored, and the game will automatically change it into species name when sending it using GTS.
As soon as you rename your Pokemon for the first time, it will never return to being without a nickname. Even if you rename it to the original name, it will still be considered nicknamed and won't change on evolution.