I suppose it just seems weird to write “//e” when it’s the “Apple two E” and II is the universally accepted Roman numeral notation for the number two.

That's how it was named. The bootscreen didn't say Apple IIe. It's Apple //e. with slashes. That's how it was in all the docs and any software and the bootrom.

Call it weird if you want, but that's what the name was.

It’s a cultural tic. Been around for decades. Those same folks also write “Apple ][“ to refer to the original Apple II.

It's a cultural tic to refer to something by its name.

You should check the actual manual: http://applelogic.org/files/AIIEREF.pdf

First, the cover uses italic sans-serif “I” characters, not forward slashes. It’s pretty clear if you’re familiar with typography.

Second, the body of the document uses neither. It uses the standard upright I character.

Is it it's name tho? Legally and culturally, do they have the power to name it?

*its

I mean, like you want to name your dog Bell character, right-to-left character, Bell character, 0-width space. Can you do that legally? Can you do that culturally? Would that become the dog's name in most of the senses?

Random characters in Apple product names is similar territory, although less extreme.