the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
It appears to be wrong to name an animal with a name that is worthy of extra respect in our religion – like the names of the Prophets and names containing the word “Allah” like `Abd Allah. This could be an insult to those names that are worthy of extra respect as a matter of faith, however unintentional the insult might be. We are supposed to show due reverence to the symbols of our faith.
Allah says: “And whoever respects the signs of Allah, this surely is (the outcome) of the piety of hearts.” [Sûrah al-Hajj: 32]
Also, it would be prohibited to name an animal in such a way that a specific person is clearly being belittled or insulted, since deliberately belittling people is unlawful in Islam.
Allah says: “O ye who believe! Let not some men among you laugh at others: It may be that the (latter) are better than the (former): Nor let some women laugh at others: It may be that the (latter) are better than the (former): Nor defame each other, nor call each other by (offensive) nicknames: Ill-seeming is a name connoting wickedness, (to be used of one) after he has believed: And those who do not desist are (indeed) doing wrong.” [Sûrah al-Hujurât: 11]
Aside from that, there seems to be no evidence that there is any harm in naming animals with whatever types of names are deemed appropriate and inoffensive according to the customs of the society in which the people are living.
The Prophet (peace be upon him) used to name his animals. For instance, he named his donkey `Ufayr. [Sahîh al-Bukhârî (2856) and Sahîh Muslim (30)]
And Allah knows best.
Source: Islam Today