I read about Hawking radiation in Wikipedia and understood black holes may disappear over a long period of time. But my question is why does it have to disappear, because after some time of radiation the mass of black hole won't be enough to maintain its "black holeness" (Hawking radiation stops) and it could become another planet or star or some other object. So Technically speaking we should be saying black holes get converted to some other object because of Hawking radiation. What is wrong in this assumption?
We need to be careful to distinguish the idealised black hole, e.g. the Schwarzschild metric, from the black holes that we might see in the real universe. The reason for the difference is that the idealised black holes take an infinite time to form so we'll never see one. For more on this see the answers to Why does Stephen Hawking say black holes don't exist?
Let's start with the idealised black hole since this is simpler. In this case all the mass is concentrated at the singularity in the centre of the black hole and the density is infinite. So as energy is lost to Hawking radiation the black hole remains a black hole since it still has an infinite density mass at the centre. All that happens is that the event horizon radius decreases.
Now a real black hole is a rather more complicated object since what we would see were we next to one is an object that isn't a black hole yet, but that is destined to become one - or at least would be destined to become one if it weren't for Hawking radiation.
The object we see has a shell of infalling matter but no event horizon. The Hawking radiation decreases the mass of the infalling matter, but the remaining matter is still on a trajectory that would form an event horizon given infinite time. So if you were able to somehow magically turn off the Hawking radiation at any point the infalling matter left would still go on to form an event horizon. Since we can't turn off the Hawking radiation what happens is that all the infalling matter radiates away before the event horizon forms. So in this case the object never forms an event horizon at all.
The error in your assumption is that a black hole has any memory of what it started out as (b.t.w. the jury is still out on that one).
From a general relativity point of view once a black hole has formed, there is no information about what it was before, as it now only carries three pieces of information, its mass $M$, its angular momentum $L$ and its charge $Q$.
The process of hawking radiation is to loose (at least) mass by radiating photons at a temperature proportional to $1/M$. This process will continue until $M$ is zero, and at no time will the black hole stop being a black hole.