Is there any named Star in the Andromeda Galaxy? or all the named stars are from the Milky Way?

No, I don't believe so, but with a little disclaimer.

Star names/designations come either from antiquity, or from star catalogs. The few hundred or so brightest stars have names that have been passed down to us, mostly from the Arabs. All those stars are in the approximately ¾ of the sky that can be seen from mid-northern latitudes. Any given star, especially the few thousand brightest ones, has several labels --

an Arabic name (Aldebaran, e.g.),

a Bayer letter (Alpha Tauri, i.e., the brightest star in Taurus, the Bull),

a Flamsteed number (87 Tauri),

a designation from the Bonner Durchmusterung catalog (BD +16º629),

the Smithsonian Astrophysical Observatory star catalog (SAO 94027),

the Hipparcos catalog (HIP 21421),

and numerous others.

At some point in the 19th century, names were given to bright stars (and constellations!) too far south to be seen from mid-northern latitudes.

All the stars that actually belong to the Andromeda Galaxy, M31, are way too faint to have turned up in any star catalogs (the "named" stars are at most, several hundred to a thousand or so lt-yr away; M31 is 2½ million lt-yr away). As late as the early 20th century, it wasn't even settled that M31 and other similar objects, were external galaxies like our own -- they were thought to be fuzzy things within the Milky Way (see "Shapley-Curtis debate").

And it was a little later in the early 20th century that individual stars were first resolved in M31, which settled that debate.

That and the Hubble relation, on redshifts of the "spiral nebulae."

Now be that as it may, M31 covers a sizeable patch of sky, and there are plenty of stars in our own galaxy that lie "in front" of it. Some of those are bright enough to appear in some of those catalogs I mentioned, and so, have designations - usually not the sort of thing you'd call a name, though. HIP 3447 is one of them, for instance. Because of their placement, they "look" like they are in the Andromeda Galaxy, but they're not, they're just along the same line-of-sight.

The other caveat is that a nova or supernova event that occurs in M31, or any other galaxy, gets a designation as, "Nova <year & sequence letter>," or, "SN <year & sequence letter>." An example was SN 1987A -- a supernova that we saw flare up in 1987 (in the Large Magellanic Cloud, which is in another part of the sky, far from Andromeda), and the first one of that year, so it got the letter, A.

http://en.wikipedia.org/wiki/List_of_stars_in_Andr...

Edit: i mistakenly refer to the constellation and not the galaxy below:

Y'know there are actually quite a few. My first guess was that you would not be able to resolve an individual star except after a supernova. But it looks like there are many. None with good names though. Great question!

Even just scrolled down the list. Apparently HD 15082 is the first star outside teh Milky we know that has a planet. You learn something new everyday!