After independence the Kingdom of Mysore became Mysore State, with Bengaluru as its capital. On 1 November 1956, the States Reorganisation Act brought the Kannada-speaking regions together into an enlarged Mysore State. That date is now celebrated every year as Karnataka Rajyotsava. The state was renamed Karnataka in 1973.
The granite Vidhana Soudha, home of the state legislature, was completed in 1956 under Chief Minister Kengal Hanumanthaiah and is the city's most recognisable building. See Vidhana Soudha.
Further reading: Vidhana Soudha on Wikipedia.