Naming the fallen child a certain name will give you unique messages after you chose the name. Some names will also do certain things. Here is a list of names that give you unique messages and do certain things:

UPDATE: I added more names to the list.

• Flowey - Message will say "I already CHOSE that name" and prevents you from using that name.
  
• METTA/METT/MTT - Message will say "OOOH!!! ARE YOU PROMOTING MY BRAND?"
  
• Alphys - Message will say "D-Don't do that" and prevent you from using that name.
  
• Alphy - Message will say "....OK????"
  
• Toriel - Message will say "I think you should think of your own name, my child" and prevents you from using that name.
  
• Sans - Message will say "nope." and prevents you from using that name.
  
• Papyru - Message will say "I'LL ALLOW IT!!!"
  
• Shyren - Message will say "...?".
  
• Asriel - Message will say "..." and prevents you from using that name.
  
• Napsta or Blooky - Message will say "............ (They're powerless to stop you.)"
  
• Frisk - Will initiate hard mode.
  
• Temmie - Message will say "hOI!"
  
• Aaron - Message will say "Is this name correct? ;)"
  
• Woshua - Message will say "clean name".
  
• Bratty - Message will say "Like, OK I guess".
  
• Catty - Message will say "Bratty! Bratty! That's MY name."
  
• Asgore - Message will say "You cannot" and prevents you from using that name.
  
• Gerson - Message will say "Wah ha ha! Why not?".
  
• Chara - Message will say "The true name". Removing the name from a save file will make the name be given by default.
  
• Gaster - Causes the game to go back to the intro, making the game not let you use that name without hacking.
  
• Bpants - Message will say "You are really scraping the bottom of the barrel".
  
• Jerry - Message will say "Jerry".
  
• AAAAAA - Message will say "Not very creative...?".
  
• Murder or Mercy - Message will say "That's a little on-the-nose isn't it...?".
  
• Drak\Gigi\Gugu - The item "Steak in the Shape of Mettaton's Face" will show as FSteak in the inventory instead of showing as Face Steak. (Credit to Kitsune Hawk for telling me this)
  

These are all of the discovered ones so far. There could be more that haven't been found yet.

Links:
http://undertale.wikia.com/wiki/Flowey#Name
http://undertale.wikia.com/wiki/Mettaton#Name
http://undertale.wikia.com/wiki/Alphys#Trivia
http://undertale.wikia.com/wiki/Toriel#Name
http://undertale.wikia.com/wiki/Sans#Name
http://undertale.wikia.com/wiki/Papyrus#Name
http://undertale.wikia.com/wiki/Shyren#Name
http://undertale.wikia.com/wiki/Asriel_Dreemurr#Name
http://undertale.wikia.com/wiki/Napstablook#Name
http://undertale.wikia.com/wiki/Frisk#Name
http://undertale.wikia.com/wiki/Temmie#Name
http://undertale.wikia.com/wiki/Aaron#Name
http://undertale.wikia.com/wiki/Woshua#Name
http://undertale.wikia.com/wiki/Bratty_and_Catty#Names
http://undertale.wikia.com/wiki/Asgore#Name
http://undertale.wikia.com/wiki/Gerson#Trivia
http://undertale.wikia.com/wiki/Chara#Name
http://undertale.wikia.com/wiki/W._D._Gaster
http://undertale.wikia.com/wiki/Burgerpants#Trivia
http://undertale.wikia.com/wiki/Jerry#Trivia
http://undertale.wikia.com/wiki/Names#Na...nsitive.29
http://undertale.wikia.com/wiki/Names#Na...n_the_game:

Additionally, (and this could work as a separate piece of trivia) if you name the fallen human "Drak", "Gigi", or "Gugu", the item Steak in the Shape of Mettaton's Face is renamed FSteak, as a reference to Gidigidi's Persona 4 Hiimdaisy comics.

Source: http://undertale.wikia.com/wiki/Names

(01-22-2016, 10:46 AM)Kitsune Hawk Wrote: Additionally, (and this could work as a separate piece of trivia) if you name the fallen human "Drak", "Gigi", or "Gugu", the item Steak in the Shape of Mettaton's Face is renamed FSteak, as a reference to Gidigidi's Persona 4 Hiimdaisy comics.

Source: http://undertale.wikia.com/wiki/Names

Thanks for the info. I'll add it to my trivia.