Some evidences that using the word Khuda (a Persian word for The Almighty) for Allah is permissible.
Abdullah ibn Mubarak, a Tabai, using the word ‘Khuda’
“And it was also narrated from Muḥammad bin Salām, who said: Faḍālah asked ‘Abdullāh bin al-Mubārak concerning the Descent (al-Nuzūl) [of Allāh] on the night of the middle of Sha‘bān. ‘Abd Allāh replied: ‘O weak one! Do you find God (Khudā, Khaddaya) to be a night-watchman (actually shab-gīr, written in Arabic as Khosheerkun)? He descends how He wills.'”
Note: By asking specifically about the 15th of Sha’ban, the questioner implied that Allah’s “Descent” is a special event limited to that night. Ibn al-Mubārak refutes this by asking, “Do you think God is a night-worker [who only shows up on this specific night]?” He then affirms the orthodox Sunni stance in the final Arabic clause: “He descends how He wills” (meaning, He is not restricted by the limits you are imposing).
Imam Ibn Taymiyyah on using the word Khuda
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: The Lord, may He be glorified, may be referred to in Arabic as Allah, ar-Rahmaan (the Most Gracious), ar-Raheem (the Most Merciful), and in Farsi as Khoda and so on, but He, may He be glorified, is One, and there are many ways to refer to Him.
(End quote from al-Fataawa al-Kubra, 6/568, translation of this quote was taken from islamqa.info)
Shaykh Zubair Ali Zai on using the word Khuda
Saheehus-Seerah 