Cat is a Taahir animal and we have many Hadeeths from the Prophet (SAWA) and his Ahlul Bayt (AS) that keeping a cat at home is allowed and performing Wudhu from remaining of water from which cat drank is allowed. About the name of a cat in the house of the Prophet (SAWA), the narration is found in Sunni books, but I could not find it till now in our Shia books. It make no difference as the Hadeeths which we have are authentic in allowing having a cat at home.
Wassalam.