Praise be to Allah.
Al-Jawaad (Magnanimous) is one of the names of Allah, as is indicated in the Sunnah. Al-Bayhaqi narrated in Shu’ab al-Eemaan and Abu Na’eem narrated in al-Hilyah from Talhah ibn ‘Ubayd-Allah and Ibn ‘Abbaas (may Allah be pleased with them both) that the Prophet (peace and blessings of Allah be upon him) said: “Allah is Magnanimous (Jawaad) and loves magnanimity, and He loves high morals, and He hates low morals.” Classed as saheeh by al-Albaani in Saheeh al-Jaami’ no. 1744.
Ibn al-Qayyim (may Allah have mercy on him) said in al-Nooniyyah:
He is the most Magnanimous and His magnanimity encompasses all of creation with bounty and kindness
He is the most Magnanimous and He does not turn away anyone who asks, even if he is from a kaafir nation.
Shaykh al-Sa’di said in al-Tafseer (5/299): al-Rahmaan (the most Compassionate), al-Raheem (the most Merciful), al-Barr (the Benign) al-Kareem (the most Generous) al-Jawaad (the Magnanimous) al-Ra’oof (the most Kind) al-Wahhaab (the Bestower) – these are all names that are close in meaning, and they all indicate that the Lord has the attributes of mercy, kindness, magnanimity and generosity, and that His mercy and giving encompass all of creation as decreed by His wisdom, and that the believers enjoy the greater part of that. End quote.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said when listing the names of Allah: From the Sunnah of the Messenger of Allah (peace and blessings of Allah be upon him) we learn the names: al-Jameel (the Beautiful), al-Jawaad (the Magnanimous) al-Hakam (the Arbiter) al-Hayy (the Ever Living). End quote from al-Qawaa’id al-Muthlaa.
See: Sifaat Allah ‘azza wa jall al-Waaridah fi’l-Kitaab wa’l-Sunnah by Shaykh ‘Alawi ibn ‘Abd al-Qaadir al-Saqqaaf.
Based on that, it is permissible to use the name ‘Abd al-Jawaad (slave of the Magnanimous).
And Allah knows best.