Radha is known as Radhikarani or Radharani because this name is given to her by her beloved love Lord Krishna. I know this answer is a little bit funny. But I will tell you lots of things for evidence. I am not wrong if I tell you that majority of you like to call your beloved by a different name which is dear to your love. Same principle applies with Krishna. He also likes to call Radha as Radhikarani or Radharani and this name sounds very pretty to Radha.
Why did Krishna lovingly say Radharai to Radha?
Here is a point never to forget that Krishna has added only rani after the name of Radha. Radha and Radhika are the original names of Goddess Radha. You can crossly ask me a question. Why did Krishna add rani after the name of Radha to call her affectionately. If you want to know it deeply you must read my previous article 'Untold Story of Radha and Krishna'. According to Google, 6813 people have read this article until the time of this article being written.
What is the evidence to support my opinion?
If you want to learn more about it, I hugely recommend my popular article ''Reality of the Story about 16100 Girls with Lord Krishna''. Enjoy reading and let me know if you have any curiosity.
Discovered by Don Prince