Hazrat Abu Huraira(RA) The father of kittens:

Hazrat Abu Hurairah (radiallahu anhu) is a famous Sahabi.The actual name for Abu Hurairah(ra) is `Abd al-Rahman ibn Sakhr Al-Azdi.

Abu Hurairah (R A) was born in Baha, Yemen into the Banu Daws tribe from the region of Tihamah on the coast of the Red Sea. His father had died, leaving him with only his mother and no other relatives. His name at birth was Abd al-Shams (servant of the sun). However, as a child, he had a cat and became known as "Abu Hurairah (R A)"
His name Hurairah is derived from the Arabic word Hirrah which means cat. He was known as the the kitten man, literally "the father of a kitten" because he was fond of cats and since his childhood often had a cat to play with.

Acceptance of Islam:

Abu Huraira became a Muslim at the hands of At-Tufayl Ibn Amr who was the chief of the tribe to which he belonged. When he submitted to the truthfulness of this religion, he accompanied At-Tufayl to Makkah and had the privilege of meeting the noble Prophet (s.a.w.). The Prophet (s.a.w) asked Abu Huraira what his name was, "Abdu-Shams" (the servant of the sun), Abu Huraira replied. So he was introduced by the holy Prophet (s.a.w) to change his name to "Abdur-Rahman" (the servant of the Beneficent). However, he continued to be known among people as "Abu Hurrah" (the kitten's father) because of his love for a cat he looked after and fed, and which used to stick to him wherever he went.

Hurairah name given by hazrat Muhammad(peace be upon him):

Abu Hurairah, famous as a companion of the Prophet (saw) and a major narrator of his sayings. Was given the nickname Abu Hurairah (literally father of Kittens) by the Prophet because he used to care for a small male cat.
there is also a related legend story in which a cat saved the Prophet's life from a deadly snake....
A snake had crawled into his sleeve and refused to leave. A cat was called and asked the snake to show its head, in order to discuss its departure. When the snake finally appeared, the cat pounced on it and carried it off.

Is it sunnah to keep a cat:

It is permissible to keep a cat as a pet, but this should not be considered a sunnah.

Having a Pet Cat permissible in Islam:

It is permissible to keep a cat as a pet. The fur of the cat touching ones clothes does not make the clothes impure. Hence,your Sal-ah will be valid.

It is narrated by Abdullah bin Rafiâ "I said to Abu Hurairah: 'Why were you given the Kunyah (nickname) Abu Hurairah?' He said: 'Do you not fear me?'" He said:"Indeed, I am in awe of you.' He said: 'I used to tend the sheep of my people, and I had a small kitten; so I used to place it in a tree at night, and during the day I would take it and play with it. So they named me Abu Hurairah.'
Love your cats ;)