Well, the “Confused” part is about simultaneously living two difference cultures, in this case Indian and American, and not being able to identify completely with either.
Parents of an ABCD would have grown up in India with a specific set of values, traditions, beliefs, etc. They come to the States to work, and end up staying there. They have kids, and naturally want to bring them up with the same set of values and belief systems that they have.
But the kids aren’t just living with their parents. They go to American schools, hang out with other American kids, and imbibe parts of the American culture too. Kinda like a neither-here-nor-there syndrome. And this stays with them even as adults. It shows up especially when they come down to India for a holiday (from my experience). Back me up, ABCDs 
And regarding Bombay and Mumbai. Mumbai was the name of this little village which existed a few hundred years ago, named after the local goddess Mumbadevi. Then the Brits came, Mumbai turned into Bombay because they had difficulty pronouncing the former, and well, the village kinda grew! That’s history. We Bombayites grew up loving the city, and even it’s name.
And then one fine day, a political party officially changed the name back to it’s original one. Their reason - the Brits left 50 years ago, but we’re still using their names. So they changed the name of Bombay. They didn’t just stop at that - a name changing spree began, and roads, museums, airports, railway stations all had their names changed!!
And we Bombayites just hate that. Officially, it’s now called Mumbai, but most Bombayites still call the city Bombay. What really rankles is that there were, and still are, a whole of lot of more important things that our representatives in government need to do for the city, but all they could think of was changing names. :mad:
Gotta mention though, locals (people from the state of Maharashtra, of which Bombay is the capital) always have called the city Mumbai. But since Bombay has as many locals as it has people from the rest of the country, you have an equal number of people using both names. Which, quite frankly, is exactly the way things were before the name was changed.
GO BOMBAY!!!
Wow!! I’m still pretty pissed about it, 7 years after it happened!!