I have heard of people putting up their house or cars, etc for auction
in order to sell it.

For example, dividing the value of the house in X shares of $5k, etc.
Then they advertise it and collect the bids, making the draw once the
value of the house is reached.
I have seen it on TV too.


I am researching this and I have a few questions:
- Does this process have a name
- Is this considered a form of gambling, and / or does an
individidual/company have to apply/register somewhere to start an
auction.
- Is the prize considered income from gambling for the winner (i.e.:
does the winner have to pay taxes on the prize)

Any information on that process is welcome, I would like to know what
I need to know in order to do the same.

You use the term auction but seem to describe a raffle.

Webster's dictionary defines an auction as:
"a sale of property to the highest bidder"

There would not be shares, or a draw in any auction.

Now a raffle is defined as:
"a lottery in which the prize is won by one of numerous persons buying chances "

In the US, Raffles are typically considered gambling and controlled at
the state level.  In most states Raffles are restricted to non-profit
organizations, with limits on who can hold them, how often and who can
profit from them.

Link:
www.m-w.com (webster's dictionary)

I was looking for the exact term used for it. This allows me to
further my research. Thanks for the information!