Some things that should probably be noted.
First, the stars in ED are a quite good representation of the real-world galaxy, at least as far as visible-in-the-night-sky-of-Earth stars are concerned. So all of the bright stars that make up the familiar and even the not-so-familiar constellations will be in-game. Example: the relatively obscure constellation Scutum. I made a side-by-side pic of it's appearance in ED and a real-world starmap:
As you can see, even the relatively dim stars of this small, unremarkable constellation (such as Zeta Scuti) have been added to the game. UY Scuti, on the other hand, is not in-game, because it's too dim to be naked-eye visible from Earth, and was not known to be "the largest star in the galaxy" at the time the ED galaxy was created.
Second, all of the bright, visible-from-Earth named stars will already have been visited, so you won't actually be "exploring" them, just visiting them. Lots of them will be within 200 LYs of Earth, so will therefore be likely to be inhabited, and therefore regularly visited by players.
Third, be aware that stars are not like people: they have more than one "name" by which they are known, and the name by which they are perhaps best known is not necessarily the name they are known by in ED. Take the Cygnus constellation: the brightest star in Cygnus is the supergiant star which everybody knows as "Deneb", but in ED, this star is known as "Alpha Cygni". If you're looking for a star and can't find it, it's probably in-game under a different name; use a reference like Wikipedia or SIMBAD to find the alternate names for the star, and look those up in ED.
Finally, some of the stars on your short-list of constellations are permit-locked. Alioth is a star in the Big Dipper; it's the Alliance capital and is permit-locked by the Alioth Independents minor faction; you will need to do some work for the Alioth Independents to become Allied with them and gain the permit before you can visit Alioth. Polaris is in the Little Dipper, and is permit-locked with a special permit that no-one yet knows how to obtain (apparently, there's something super-secret and Thargoid-related going on down there), so you won't be able to visit Polaris at all.