The word "areesh" means a shaded structure, a canopy, or similar things. It is permissible to use the name Arishaa (عریشا). However, it is better to choose a name from among the names of the Sahabiyat (may Allah be pleased with them), because the Prophet ﷺ counted giving children good names among the rights that children have over their parents.
One hadith states: It is narrated from Hazrat Ibn Abbas (may Allah be pleased with him) that the Sahabah Kiraam (may Allah be pleased with them) said: "O Messenger of Allah, we have learned what rights a father has over his child, so tell us what rights a child has over his father." The Prophet ﷺ replied: "That he give the child a good name, and that he raise them with good character."
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
شعب الایمان: (رقم الحدیث: 8658)
عِنِ ابْنِ عَبَّاسٍ رضی اللہ عنہ :أَنَّہُمْ قَالُوْا یَا رَسُوْلَ اللّٰہِ! قَدْ عَلِمْنَا مَا حَقُّ الْوَالِدِ عَلَی الْوَلَدِ فَمَا حَقُّ الْوَلَدِ عَلَی الْوَالِدِ؟قَالَ أَنْ یُحْسِنَ اِسْمَہ‘ وَیُحْسِنَ أَدَبَہ‘۔
تفسير الطبري: (585/4، ط: دار هجر)
وَأَمَّا الْعُرُوشُ: فَإِنَّهَا الْأَبْنِيَةُ وَالْبُيُوتُ، وَاحِدُهَا عَرْشٌ، وَجَمْعُ قَلِيلِهِ أَعْرُشٌ، وَكُلُّ بِنَاءٍ فَإِنَّهُ عَرْشٌ، وَيُقَالُ: عَرَشَ فُلَانٌ دَارًا يَعْرُشُ وَيعْرِشُ، وَعَرَّشَ تَعْرِيشًا وَمِنْهُ قَوْلُ اللَّهِ تَعَالَى ذِكْرُهُ: {وَمَا كَانُوا يَعْرِشُونَ} [الأعراف: 137] يَعْنِي يَبْنُونَ، وَمِنْهُ قِيلَ عَرِيشُ مَكَّةَ، يَعْنِي بِهِ: خِيَامَهَا وَأَبْنِيَتَهَا.
مجمع بحار الأنوار لمحمد طاهر الفَتَّنِي: (556/3، ط: مطبعة مجلس دائرة المعارف العثمانية)
وكان المسجد على "عريش"، هو ما يستظل به والسقف والخشب، أي لم يكن له سقف يكن من المطر.