Nama-karana ~ is a different samskara than diksa!
1.
Srila Bhaktisiddhanta Saraswati Goswami Thakur has written the following comment in his Anubhasya (Chaitanya Charitamrita 2.1.208): “Mahaprabhu showed his mercy to Dabir Khas and Sakar Mallik by giving them the spiritual names of Rupa and Sanatan, respectively. Nama-karana is a type of samskara on the lowest level of qualification. However, those who ignore the mercy that is manifest in the spiritual name have no chance of attaining devotion to Krishna, but remain intoxicated with material prestige.”
Amongst the Lord’s companions present on this occasion were Nityananda Prabhu, Hari Das Thakur, Srivasa Pandit, Srila Gadadhara Pandit Goswami, Mukunda Datta, Jagadananda Pandit, Murari Gupta, Vakresvara Pandit and many others. The Lord had them all give their blessings to Rupa and Sanatan.
2.
Vrindavan Das Thakur also confirms definitively that Rupa was named Dabir Khäs and Sanatan, Säkar Mallik.
In the Çeña-khaëòa [of the Chaitanya Bhagavat], the Lord revealed himself to Dabir Khäs and recognizing their greatness, released them from their bondage. He then named them Rupa and Sanatan. (Chaitanya Bhagavat Adi Kanda 1.1.171-2)
Then, two great fortunate souls came to the spot where the Lord was. The two brothers were named Säkar Mallik and Rupa. The Lord looked upon them with compassionate eyes. (Chaitanya Bhagavat Antya Kanda 3.9.238-9)