What's the name of these "banners" used in Japanese restaurants?

In Japanese, it's called a noren (written 暖簾 in Japanese orthography).

English doesn't have a common term for noren, so the word has been borrowed into English, but if you use it in English you'll probably have to define it so your audience knows what you mean. You can see this sort of use on the English Wikipedia page for noren:

Noren (暖簾) are traditional Japanese fabric dividers, hung between rooms, on walls, in doorways, or in windows. They usually have one or more vertical slits cut from the bottom to nearly the top of the fabric, allowing for easier passage or viewing. Noren are rectangular and come in many different materials, sizes, colors, and patterns.

Since the loanword noren isn't known to most English speakers, phrases like shop curtain or noren curtain are sometimes used in English instead, but unless the reader is familiar with the type of curtain you're talking about, it's likely to be unclear without further explanation.

You can see more examples of what qualify as noren in a Google Image Search for 暖簾.

This specific example you gave is a “restaurant menu” from the Kukuru restaurant in Osaka Japan. Or, basically they are “signs”, or “signage” in English. (or as you simply state, "banners".)

Menu - 1.) a list of the dishes served at a meal; bill of fare: 2.) the dishes served.

Sign - 5.) a notice, bearing a name, direction, warning, or advertisement, that is displayed or posted for public view: