Praise be to Allah.
There is nothing wrong with giving animals appropriate names. Al-Bukhaari (2872) narrated that Anas (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) had a she-camel called al-‘Adba’, that was never beaten in a race.
Al-Bukhaari (2627) and Muslim (2307) narrated that Anas (may Allah be pleased with him) said: There was a disturbance in Madeenah, and the Prophet (blessings and peace of Allah be upon him) borrowed a horse belonging to Abu Talhah that was called al-Mandoob, and rode it. He said: “We have not seen any cause for panic, and we have found it (the horse) to be swift-footed.”
Al-Baghawi (may Allah have mercy on him) said:
This shows that it is permissible to name animals; it was the custom of the Arabs to give animals and weapons names by which they would be known if they were to look for them, apart from ordinary names (nouns).
End quote from Sharh as-Sunnah, 8/222
al-Bukhaari gave this chapter the title: Chapter on Naming Horses and Donkeys.
Then he narrated a number of hadeeths concerning that, such as the hadeeth which says that the Prophet (blessings and peace of Allah be upon him) had a horse that was called al-Laheef (2855), and he had a donkey that was called ‘Ufayr (2865).
Al-Muhallab said: The fiqh concerning this matter is that it is permissible to give names to animals other than what they are usually called.
End quote from Sharh Saheeh al-Bukhaari, 5/60
Abu’d-Darda’ had a camel called Damoon. Narrated by Ibn al-Mubaarak in az-Zuhd, 1173
Abu Qataadah had a horse called al-Jaraadah. Narrated by al-Bukhaari, 2854
Al-Manaawi said, after mentioning some of the reports that were narrated concerning this matter:
This shows that it is acceptable in sharee‘ah to give names to horses, mules, donkeys and other animals by which they may be told apart from others.
End quote from Fayd al-Qadeer, 5/220
See: Zaad al-Ma‘aad, 1/132-134; al-Mawsoo‘ah al-Fiqhiyyah, 11/338
And Allah knows best.