Supposedly, "bit" is short for "binary digit", so we'd need a separate term for "ternary digit", but I don't wanna go there.

The prefix is tri-, not ti- so I don’t think there was any concern of going anywhere.

It’s tricycle and tripod, not ticycle.

The standard term is "trit" because they didn't want to go there.

Ternary computers have 8 tits to a byte.

Should be either 9 or 27 I'd think.

Why can’t it be 8?, the fact that it’s a trit doesn’t put any constraint on the byte (tryte ? size). You could actually make it 5 or 6 trits (~9.5 bits) for similar information density. The Setun used 6 trit addressable units.