If he's already named his Chocobo then he's done all that. You can't name him until you turn in the 2000 seals and finish the quest.

Make sure you go into your inventory and find the Chocobo Whistle. "Use" it. This will give you the ability to call him. From there you can call him either under Actions or Mounts in your menu. That will allow you to ride him. It will be the same with Barding when you get those, as well as with Minions. To call/use them you must first find them in your inventory and select "Use". That will then allow you to call the Minion, or change your Chocobo Barding, as the case may be.

Now, as for fighting with him, I don't know if you can do that right away. You probably can, but since you can't level him up until level 30 I usually just wait till then and not waste the greens. At level 30 Ducette in Camp Tranquil will start the quest that allows you to level your Chocobo.