Humble Pranams,
1. Prof TMP Mahadevan, Dept of Philosophy, University of Madras, in his scholarly work 'The Philosophy of Advaita with special reference to Bharatitirtha Vidyaranya' has discussed this topic at length. The gist of his argument is that Vidyaranya was not a personal name. It was an appellation or surname used by both Swami Bharati Tirtha and his disciple Madhav. So we have Bharati Tirtha-Vidyaranya and Madhav-Vidyaranya. He further mentions that the colophon to one of the manuscripts of Panchadashi in Tanjore palace attributes the authorship of the book to Bharati Tirtha -Vidyaranya, (a single person) This shows that Bharati Tirtha might have had the surname Vidyaranya.
2. Prof V B Joshi in his doctoral thesis on 'Vidyaranya's contribution to Advaita' assumes the identity of Madhav the brother of Sayana with Vidyaranya. However he does not look upon 'Vidyranya' as an appellation or surname. He assumes it to be the personal post sanyasa name of Madhavacharya.
Prof. Joshi continues- Madhavacharya-Vidyaranya was the disciple of both Vidyatirtha and Bharatitirtha, who were successive pontiffs of Shrungeri Matha. Madhavacharya, who initially led the life of a householder, took Sanyasa in 1374 after the death of Bharatitirtha was installed as the pontiff of Shrungeri Matha.
Regarding the authorship of Panchadashi, Prof Joshi concludes, citing Ramkrishna, a direct disciple of both Bharati Tirtha and Vidyaranya-
A. Panchadashi has dual authorship.
B. The chapter Trupti Deepa is written by Bharati Tirtha
C. Rest of the chapters have been written by Vidyaranya
D. Dr Gundappa opines that Deepa Panchaka was written by Bharati Tirtha and Viveka Panchaka and Ananda Panchaka was written by Vidyaranya.
3. Nishchaladas in his 'Vrutti Prabhakar' ascribes the authorship of the entire Panchadashi to Vidyaranya.
Hope this helps.
Ravi Shivde