For most Fanfics usually you give the story a name and then put in parenthesis on the side that the story is naruhina or naruxhina which ever you prefer. Or sometimes you just tag the story as a naruhina story.
-In Story Critique-
You do randomly change tenses from time to time and that needs to be fixed.
Purtana should be capitalized.
Hinata does usually stutter, but I don't think I've seen her really stutter a lot except when she's trying to say something to Naruto. Usually she's just quiet and not very assertive.
Give us a little more detail about the lady hobbling around and such. If it is a message from the hokage though, they usually come through ANBU members or other faster youthful characters. If Purtana is old and doesn't get around easily, there isn't much of a chance she could make it to the Hokage and back in one piece.
Thank is spelt with a k on the end
smile If the Hokage needs to see Hinata, usually character's hurry to see the Hookage instead of calmly walking over.
The hokage's office isn't at the academy, unless you've changed the village's layout, in which you should specify that a little.
I would use a describing verb like beat when talking about Hinata's heart because you used went in the beginning of the sentence.
You're needs the apostrophe so that the sentence is gramatically correct
For Tsunade to say that she "needs" to keep the something simple it sounds like she's under pressure and needs to hurridly send the couple off on a mission, but I feel that the situation you've created is missing that tension to match the speech.
Cloud's should be capitalized and needs an apostrophe
women should be plural
(your i's need to be capitalized)
-Overall Critique/Tips-
Your story sounds like it could be interesting, but your characters and story line are a little out of balance.
This should be more of an intense grab your reader's interest and I can see the potential sleeping here in your writing, but you aren't accessing it as effectively as you can.
You also I feel aren't really capturing the character's personalities as they should be. Naruto usually complains about what ever Granny Tsunade tells him to do (unless it's an A-rank mission, cause then he feels important) and usually he laughs and makes jokes at Hinata, clearly misunderstanding her blushing and embaressed pushing her index fingers together.
Most missions are carried out in teams, teams usually consist of 4 people. It is possible to still write a Naruhina story while having the couple go out on a mission with another couple/group, you can just seperate them into two scouting groups when they make it to the hide out.
Your story does have a bit of a checklist feel to it. She did this, then she did this and then she did this. He did this. She did this. (check check check check check)
Smooth it out a little by giving us a couple of extra details and foreshadowing about what could possibly happen. Use descriptive verbs to describe actions and try not to repeat them again in a paragraph. Expand conversations a little so that they seem more life like.