Kumars are common last names (tribal names) prevalent in mostly cow belt areas like UP and Bihar and to some extent Delhi and Haryana as well.
They used to be primarily agriculturist mid level tribes, but lately in the 18th and 19th centuries they largely got educated and moved up in Indian society via administrative roles in govt. etc. I doubt they are a Brahmin level caste. Brahmin educated folks typically go into far higher administrative and academic pursuits than go into Indian Defence Force hierarchy. Unless its a family thing where your dad was in the armed forces as well.
North Indian Hindu Brahmins have typical names like this according to geographic areas in India, South Indian Brahmin namess are another ball of wax altogether (the list below is not all inclusive):
(Uttar Pradesh) Sharma, Dwivedi, Dubey, Trivedi, Tripathi, Tiwari, Chaturvedi, Choubey, Pande, Mishra, Garg , Bharadwaj, Sandilya,
(Uttarakhand) Joshi, Kesari, Pant,
(Bihar) Jha & Ozha,
(Punjab &Haryana) Upadhyaya, Bahuguna , Vashist,
(Bengal) Chattopadhyay (Chatterjee) , Gangopadhyay (Ganguly), Mukhopadhyay (Mukherji) Bandophadyay (Banerjee) and Bhattacharya,
(Assam), Goswami
(Maharashtra) Puranik, Kulkarni, Deshmukh, Sardesai, Pandit, Karve, Chitale, Godbole, Shrikhande.
Kumar is not a traditionally common Bengali name or even South Indian name to my knowledge.
The word "Kumar" in Bengali means young man, bachelor, son, boy etc. Similarly - "Kumari" means young girl.
In Bangladesh the word "Kumar" also is a common name for potter. Like in English the last name "Smith" means Iron-smith - who make knives and swords,
@Atlas bhai your thoughts?