As a native English speaker (American), I have never heard someone say "That is my own sofa".
Perhaps in excitment "I own that sofa!", or "I have my own sofa!" (if it's the first one they ever bought for example).
It would be convenient if the literal German translation worked in English, but I think "own" is should be removed here.
There's a large number of Duo sentences that are equally likely (or "likely") to be heard in either language - this could be one of them. I forget what skill this sentence comes from, but translating "eigenes" as "own" is useful for teaching us how to use possessive+eigene.
Anyway, if you need an example, I could imagine a student in a dorm room, a lodger in a boardinghouse or the tenant of an apartment that came semi-furnished saying this (but maybe the latter scenario is just a weird New Zealand thing).