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.