Yup, the only difficulty with repeating it in Morse, is how you represent it. Hyphens or underscores for inter-character spaces? And how do you represent word-breaks? I like the idea of the "English" name simply because it shows some understanding on our part, rather than just repeating the Morse signal back, but at this stage all tests are good, up to and including poking it with a stick.
So far each of the Google links I've clicked for morse translation use the . - / configuration, although some don't use the /