I think I made a mistake.
A Brahman is usually known by his caste name: for Rarhis, these are generally Bandyopadhyaya (Bannerjee), Chattopadhyaya (Chatterjee), Gangopadhyaya (Ganguly), Mukhyopadhyaya (Mukherjee), Bhattacharyya, or Chakravarti. For Barendras, these names can be Bagchi, Bhaduri, Ghoshal, Lahiri, Maitra and Sanyal. For Vaidik, it is generally Chakravarti.
For gotra, the typical names are the names of rishis from whom the gotra holder claims direct, uninterrupted descent. For instance, my gotra is Kasyapa; my mother, before she married, was Dhanvantari (women 'go' to the gotra of their husband).
Among Brahmins, Bannerjees are Sandilya gotra; so the name is not the gotra, the gotra is different. Chatterjees are Kasyapa; while we share a gotra name with the Chatterjees, we are not Brahmins.
I had never heard of Debnath as a Brahmin name before, but I may be wrong. Definitely not a gotra name; never heard of Rishi Debnath, while Dhanvantari, Kashyap, Maudgalya and Sandilya are well known.
What I was trying to say was that Debnath is neither a caste name nor a gotra.
Okay, my mother's people were Ray Chaudhury, but that was a Padabi. Their caste name was SenGupta.