Even countries that use the same calendar don't call it the same thing!
Korea and Vietnam each have their own Korean and Vietnamese New Years, but Malaysia literally calls it Tahun Baru Cina (I'll give you three guesses what Cina means). In fact, several countries call it something like that: Singapore and the Philippines calls it the Chinese New Year, Brunei calls it Tahun Baru Cina, etc. Meanwhile, China doesn't even call it a lunar new year, they call it the spring festival.
Lumping them all together is just something we're doing to make it easier for Americans.
Korea, Malaysia, and Singapore don't call it the same name because they speak different languages, but they do not all call it Chinese New Year in real life, no matter what your Google Fu says.
I'm speaking to this from China right now, saying Happy New Year every 10 minutes. China is one of the countries with a literal lunar calendar.
Lunar New Year is perfectly accurate, and more accurate than "Chinese New Year".
My Korean is terrible, but when I was there they all said sollal, the local name of the lunar New Year holiday.
Vietnam was easier because the lunar New Year is called the pronounceable "tet."
Malaysia, Singapore, they have local names for the lunar New Year that don't include the word China.
You're really hunting for these "Chinese New Year" names that are in practice uncommon or disused.
You can call it that if you want to, but you'll just be that old grandma in the meme with the hospice worker assuring you that everything is fine and she can escort you back to 4chan.
In fact, please go to any of the countries you've mentioned, or Singapore or the Philippines and tell them that you're celebrating Chinese New Year and report back their response.
Especially the Philippines, they don't brook no s*** hahaha.
The "tahun baru cina" thing used in Malaysia, Singapore, Indonesia and Brunei isn't uncommon or disused btw. It's the term used by the native Malay population because Malay is the official language in those countries. A term not used by the cultures celebrating this lunar new year.
I have not heard that term during the lunar New Year, and I've heard people say Happy New Year in Malaysia hundreds of times.
If you're a native Malay, I will take your word for it that your particular village(which village are you from ?) is peculiar, since that is not the common national phrase.
You don't sound like a native malay.
You have way too many native English joinders to be a Malay.
Are you searching Google for any international phrase that connects to China so that you're not completely wrong about this, even though you were completely wrong about this?