Can I Use Same Name As Other Company If The Name Is Too Common Or English Word?

Hey, I'm not sure if this is the right place but I'm very confused and haven't been able to figure this out right so I'm asking here.

Using RAINBOW only as an example.

Let's say there are many companies around the world with the name "Rainbow" which is also a common English word.

Now let's say my last name is Rainbow and I wanted to open a business, a company in tech field or fashion industry and name my company Rainbow. Could I do that? I've seen many business with the name lets say Rainbow, many many ones, even many ones in the same country, and they operate just fine.

But in case the company becomes something major and international, would it create any problem?

I just wanna use the name "Rainbow" but i'll have own logo and own things, all original.

Is it possible?

Another question: In such cases, names like this, Rainbow and all, let's say trademarked or legally registered copyrighted or whatever they do, if it's not yet trademarked and all that, but many companies already exist with the name, or another company comes up with the same name, do they get any legal issue for the name from other companies using same name?

Or any type of problem or issues one might face if they use the name Rainbow?

notes: using rainbow as an example, but the actual name that I really don't want to share, there are many companies with that name, but none of them are huge like Facebook or something, lol. but there are many, and even in the entire world, like every place. And it is an actual english word like Rainbow, Sun, Day, Moon, Queen.

I know having new unique name is better I really really wanna use my real/legal last name and I need to be sure and thats why I'm asking you guys. please help me understand and try to explain if there's any way I could do it and avoid issues.

thank you so much.