THERE IS AN ISLAND AT LATITUDE70.0167 LONGITUDE 21.1000 ALTITUDE FEET
0 IN NORTHERN NORWAY WITH MY NAME MAKSTEIN ISLAND. IS IT INHABITED?
HOW DID IT GET ITS NAME

The given coordinates do refer to an island in northern Norway, but
its name is not "Makstein".  According to official Norwegian
large-scale maps its name is "Hakstein" (in Norwegian) or "Arasgædgi"
(in Sami).  Hakstein is located 4 km east of the small town Skjervøy
in Troms.  It has a small mountain (73 m above sea level) and is
mostly birch woods and bogs.  The maps I have access to do not show
any houses on the island.

I have called the municipal office in Skjervøy.  They confirm that the
island is not inhabited.  As for its name, the person I spoke to
thought the name refers to the island's shape when viewed from
Skjervøy - its mountain resembles a hook (which is "hake" in
Norwegian), and "stein" means "stone" or "rock".

As another researcher has pointed out, "Makstein" is a likely
rewriting of "Måkstein".  In Norwegian, "Måkstein" means "Seagull's
rock".  There are several islands and rocks along Norwegian's
southwestern coast with names that are derived from "Måkstein":

- Måksteinen (near Bømlo)
- Måksteinane (two islets near Austevoll)
- Måksteinholmen (another islet near Austevoll)

If you would like me to perform further research on any of these
islands, please post this as a new question.

A possible clue:  The name of the island may actually be "Måkstein". 
I've found only one reference to "Makstein" as the name of the island,
but a few pages in Norwegian that refer to "Måkstein".  (I'm not
certain whether these pages are referring to an island, since I don't
know Norwegian.)

A guess about the name:  Since Norwegian is a Germanic language, the
island "Makstein" (or "Måkstein") might have a derivation similar to
the surname "Makstein".