The short and simple® answer is yes, your brand name does need to be short.
At least we think your brand name needs to be short, and this is why:
Short names are easier to remember, so they require less repetition until people remember them. Once people remember a brand’s name, they can tell other people about the product or service and identify it.
Short names are less likely to be misspelled, although this is actually less important nowadays as in most cases Google will correct misspelled brand names pretty quickly.
Short names are easier for designers to work with too, long names require long spaces or small text size.
How many of the brands you know and love, or hate, have names which are longer than 10 characters? It is probably a lot less than 10 percent, and there’s a reason for that.