Arish is an indirect Quranic name for boys that means one who is working on and building something great, such as a tall or complex building, system or project. It comes from Arsh, which means throne, or a structure that has taken a lot of effort to build and is derived from the Ain-R-Sh (throne, to build) which is used often in the Quran.
And after they had entered the city, Joseph raised his parents to the throne beside himself, and they (involuntarily) bowed in prostration before him. Joseph said: “Father! This is the fulfilment of the vision I had before – one that My Lord has caused to come true. He was kind to me when He rescued me from the prison, and brought you from the desert after Satan had stirred discord between me and my brothers. Certainly my Lord is Subtle in the fulfilment of His will; He is All-Knowing, All-Wise. (Quran 12:100)
Your Lord inspired the bee, saying, ‘Make your homes in the mountains, in the trees, and also in the structures which men build. (Quran 16:68)
Arish is also a Farsi name meaning wise and intelligent. It is not related to the Quranic word but since the meaning is good Muslims can use it.