Kan: ಗದಗ-ಬೆಟಿಗೇರಿ gadaga-beṭigēri
‘Rocky Road-Hill Tank’ [Kaldugu] -City/District, Karnataka
From Kan: kal, ‘stone’, ‘boulder, ‘pebble’; Skt: durga, (difficult, uneven) road; ‘(inaccessible) place’; Kan: beṭṭa, ‘hill’; and kere/gere, ‘tank’, ‘reservoir’.
The Kalyani Chalukyas built fifty or more temples here in the 11-13thC featuring ornate pillars and beautifully carved sculptures. The Sri Trikuteshwara Temple has three Shiva lingas on a single stone.
This is a twin city, hence the double-barrelled name.
For related place names see Indian Place names and Karnataka place names.

Sri Trikuteshwara Temple, Gadag-Betageri Ms Sarah Welch