you can wear the ring. you could enchant it to protect you. you cannot use it to contact your 'Dragon companion' which isn't an actual thing. the statue as a medium is a neat idea, some people also use crystals, stones, sometimes incense, never tried it really myself, but you can 'call' to them through meditation, there's also a spell to bring them to you, but i feel that's a short cut. you don't really need one unless you have trouble communicating/seeing dragons.
now, dragon companion, you probably mean dragon guide, maybe dragon guardian, they are two very different things however. a dragon guardian [while probably sounds cooler] is a young dragon that stays in your house keeping out unwanted visitors, and entertaining you when the cable goes out. the dragon guide is an adult dragon you meet in the astral who will teach you. both of these dragons though don't get handed to you after choosing to do Dragon Magick, nor after getting a ring. like i said there is a spell to call to them, but that's a last stick effort that takes about a month to complete, and it's not a guarantee. Dragon Magick requires a great amount of patience, you can meet dragons, wandering dragons sometimes stop in peoples houses for a while, but unless they say 'hi, i'm your guardian' don't assume they are. when you are ready, the dragon will come to you.
my advise with that ring, put a protection spell on it so it'll be a protective charm for you. Dragon's Light Protection chant is one of the first spells i ever received, and i've done it once a month for 8 years now, you should enchant the ring with it. be sure you purify and charge it before the full moon.