حدثنا يحيى بن بكير حدثنا الليث عن يونس عن ابن شهاب قال أبو سلمة إن عائشة رضي الله عنها قالت قال رسول الله صلى الله عليه وسلم يوما يا عائش هذا جبريل يقرئك السلام فقلت وعليه السلام ورحمة الله وبركاته ترى ما لا أرى تريد رسول الله صلى الله عليه وسلم يرى جبريل وهي لا تراه
Translation: Yehya the son of Bkeer told us that Al-Laith told them from Younes from Ebn-Shehaab that Abu-Salama said that 'a'isha (radiyAllahu 'anha) said that the Messenger of Allah (sallAllahu'alayhi wsallam) said one day: "O 'a'ish, this is Jibreel tells you al-salaam (greeting)" So I ('a'isha) said: "W'alayhil-salaam warahmatullah wbarakatuh (and upon him be peace and mercy of Allah and his blessings). You (the Messanger of Allah (sallAllahualayhi wasallam)) see what I don't see (she meens Jebreel)" (Source sahih al-Bukahri)
In this hadith, the Messenger of Allah (sallAllahualayhi wsallam) called 'a'isha: ('a'ish) without the last "a", and this is in Arabic is called "tarkheem" (apocope) that you remove the last "a" of the woman name (the majority of women names in Arabic has a last "a"), and that is done to make it like a pet name.
روى النسائي من طريق أبي سلمة عن عائشة قالت: دخل الحبشة يلعبون فقال لي النبي صلى الله عليه وسلم: يا حميراء أتحبين أن تنظري إليهم. فقلت: نعم
Translation: Al-Nisa'y narrated from the way of Abi-Salama from 'a'isha that she said: Abyssinians entered as the are playing (with bayonets for training) so the Prophet told me: "O Homayraa' (little reddish), do you like to watch them?" I ('a'isha) said: Yes.
So the Prophet (sallAllahu'alayhi wasallam) called 'a'isha "Homayraa'" (little reddish, and Arab called a white woman to be red not to be confused with the whiteness of leprosy) and he called her like that petting her.
روى أحمد عن عائشة قالت يارسول الله صلى الله عليه وسلم كل نسائك لها كنية غيري فكناها "أم عبد الله
Translation: Ahmed narrated from 'a'isha that she said: "O Messanger of Allah (sallAllahu'alayhi wsallam), All of your women has a konya (another way to call a person in Arabic without calling his name directly so it gives him respect, mostly Abu- (for men, means the father of) or Ommu- (for women, means the mother of)) except me" so he gave her the konya "Ommu-Abdillah".
So he gave his wife a konya because she was sad she didn't have akonya because didn't have child.
So from this we find out that you can give your wife a nick name on condition it is a good name that doesn't make her ashamed or doesn't annoy her or isn't ridiculous. Allah said in Al-Hojorat(49th) Sura in the 11th Ayah:
In this Ayah Allah (subhanahu wt'ala) orders believers that no group (of men) scoffs at another group (of men) because it may well be that the latter (at whom they scoff) are better than they (those who scoffed), nor that a group of women scoffs at another group of women because it may well be that the latter (at whom they scoff) are better than they (those who scoffed), and not to taunt one another, and not to revile one another by nicknames, and tells that it is an evil thing to gain notoriety for ungodliness after belief, and that those who do not repent are indeed the wrong-doers.
We learn from this ayah not to revile one another by nicknames.
And Allah knows best.