The three-letter airport code is SGN. In fact, District 1 of the city is still officially Saigon. So go ahead and say it. So yeah, it's unlikely to offend anyone.
The Vietnamese nation seems to have quickly and resiliently left the war behind it, with people in both the North and South cheerfully selling wartime propaganda poster prints and even using the era as a theme in cafes. The names, Ho Chi Minh City and Saigon, are also used interchangeably throughout the country, with little mention of their origin. In short, although the background of these names was once a sensitive topic, now the two seem to be synonymous. Is it offensive to call either name? No, not at all.
The two names do not make any kind of political statement; we use them only as a habit of speaking. If you stay in the south of Vietnam, the name “Saigon” would sound more familiar and affectionate. However, people from other areas will prefer to use the official name of Ho Chi Minh City. As if it weren't confusing enough, the use of “Saigon” is also different for many locals.
If locals live in the city, they will interpret “Saigon” as “District 1 in Ho Chi Minh City. But if the locals come from other regions and don't live in the city, they will associate “Saigon” as “Ho Chi Minh City.