Both names are widely used.
Hope you enjoy your trip nyc. Have you got your visa sorted? My first trip was marred because i got to the airport before realising I needed one, and they wouldn't let me fly to arrange one at HCMC airport. I am so used to no-visa or visa on landing I didn't even think about it.
It only took a few hours to get one one on the net, but I had to rebook my flight. It is all just a money-making gambit. They charge you $US20 to pre-approve the visa on the net, and then you have to get one at the airport in HCMC or Hanoi anyway. Another $50 USD US. And if you don't take a spare passport photo with you, they are happy to charge a few bucks to take one too.
It is definitely the slowest airport I have experienced in Asia. Most Asian airports are so good now you get used to just zipping through them. It takes less than 10 minutes to check in at Changi, KL, Bangkok or Beijing, and landing formalities are just as quick. But they are still 'old school' in Vietnam. Long lines, lots of stamps, lots of peering at your photo to make sure you're you sort of thing.
I found HCM itself pretty hectic, and there are not really that many 'attractions' as such. But the further you get out of the city, the calmer and prettier it gets. Watch out for the scooters.
The trick to crossing the road is walk slowly, but don't stop. If you stop or look like you may go back, the traffic won't know what to do, and that's when accidents happen. If you remain predictable, the traffic will miss you. Waiting for a gap in the traffic is not an option unless you're prepared to wait for 3 am next Sunday morning.