But maybe some people can argue that having similar name to bitcoin can make people get confused about it.
Exactly that's my problem with "bits". Some could, for example, argue that "bit" could also simply be a short form of "Bitcoin". And then you have a new source of confusion, even for possible scam attempts.
There was another idea which was the "Hal" or the "Finney" for some small unit (I guess it was
10 satoshis according to the Bitcoin wiki, although other sources claim it's the "Finney" is worth 10,000 satoshis). This is better in my opinion, because it is distinctive. However, at least the 10-satoshi unit imo is innecessary. If the "Finney" was worth the same as the "bit", i.e. 100 sats, or alternatively 1000 sats, then I'd support it because it would occupy a space close to current fiat units.
But I stand by my stance of the previous post - I think "Bitcoin" and "Satoshi" are largely sufficient.
PS: If Bitcoin really gets significantly above the 1 million USD mark, then thinking about smaller units than the satoshi could be necessary. So we could imagine a "Satcent" (1/100 sats). I don't really like the "msats" of the Lightning Network, but they have got some acceptance now so I'm nobody to interfere there ...