Hebbar Iyengar is attributed to a Group of Karnataka SriVaishnavites.
It is generally accepted that SriVaishnavism in Karnataka (Mysore State) came into being when the Great SriVaishnava Acharya Sri RamanujaAcharya settled in Thirunarayanapuram (Melkote) -Pandavapura, Mandya District for more than 20 Years.
Many of his disciples had also followed him to Melkote. The Local Brahmins of the area had converted to SriVaishnavism during that time. Sri RamanujaAcharya affectionately called them "hebbu haaruva" meaning Elderly Brahmins.
The etymology of Hebbar, in Kannada, resolves to "hebbu/hiridhu" (elderly) + "haaruva" (brahmin). This is generally accepted.