In the Chaitanya Charitamrita (1.12.83), it is said that Uddhava Das is a branch of Gadadhara Pandit Goswami. As such, he is mentioned by Yadunatha Das in the Shakha-nirnayamrita (35):
ati-dinajane purna-prema-vitta-pradayakamWhen Rupa Goswami was old and living in Vrindavan, he was desperate to see the deity, but unable to go to Govardhana because of his advanced years. At this time, Gopal came to stay in Mathura at the house of Vitthalanatha, the youngest son of Vallabhacharya, ostensibly out of fear of possible attacks by the Muslim iconoclasts. Rupa Goswami thus had the opportunity to see Madhavendra Puri’s deity. Uddhava Das was amongst the devotees who stayed with Rupa at Vitthaladeva’s house for an entire month on this occasion.
shrimad-uddhava-dasakhyam vande’ham guna-shalinam
I venerate the highly virtuous Uddhava Das, who gave the wealth of love to those who were most fallen.
Uddhava Das lived in Vrindavan. When Srinivas Acharya and Raghava Goswami were touring Vraja dham, they came to his cottage. He greeted them with enthusiastic hospitality. Uddhava Das was amongst the devotees who gathered to wish Srinivas Acharya, Narottama Das Thakur and Shyamananda Prabhu as they set off for Bengal with the books which had been given to them by Jiva Goswami.
According to the Gaudiya Vaishnava Abhidhana, there are at least two devotees named Uddhava Das. One was a follower of Sanatan Goswami who worshiped in Vraja on the banks of Pavana Sarovara; another was an initiated disciple of Radhamohana Thakur who wrote many songs about Radha-Krishna lila. He lived in Murshidabad district in the village of Öeïagram. His real name was Krishnakanta Majumdar.
[Excerpted from "Sri Chaitanya: His Life & Associates" by Srila Bhakti Ballabh Tirtha Maharaj]