Question Summary:
Can we keep the names Arafah and Ayat for girls?

Question Detail:

Can we keep the names of baby girls Arafa and Ayat? Please advise with their meanings and if it will have a good effect?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
The word Arafah (عرفة) comes from the root letter Araf ) (عرف which means to recognise [1].
The word Ayah (آية) means a sign [2].
It is permissible to keep the above two names.
You may refer to the following link regarding keeping good names.
http://askimam.org/public/question_detail/33958
And Allah Ta’āla Knows Best
Bilal Ishaq (Issak)
Student Darul Iftaa
Leicester, England, UK 
Checked and Approved by,
Mufti Ebrahim Desai.
 [1] Hans Wehr page 709
القاموس المحيط (ص: 837)
وتَعارَفوا: عَرَفَ بَعْضُهُمْ بَعْضاً، وسَمَّوْا: عَرَفَةَ، مُحَرَّكَةً، ومَعْروفاً وكَزُبيْرٍ وأَميرٍ وشَدَّادٍ وقُفْلٍ
المعجم الوسيط (2/ 595)
و (يَوْم عَرَفَات) الْيَوْم التَّاسِع من ذِي الْحجَّة
(عَرَفَة) عَرَفَات
[2] Hans Wehr page 46