PJ. The AXAF was renamed way back when to CHANDRA, and the catalogue of stars that all such probes use is the GSC (Hubble Guide Star Catalogue), and therefore any star in the list would have a GSC catalogue designation, and the one that fits the co-ordinates that you have given in your previous post should be:
GSC1-2901099 and the Declination co-ordinates should be preceded by a plus (+) symbol as the star is higher than the celestial equator. No Star in the GSC corresponds to a negative (-) declination for those co-ordinates. From what I have been able to glean about it, this star is an A7II Giant located some 825 light years from Earth +/- 5%. The Star is a spectroscopic binary with the primary, the one we see, having a mass of 11 times the Sun and the secondary component having a mass 5 times the Sun's mass and spectroscopic studies indicate that it is a G6III subgiant. The secondary orbits the primary in a period of 3 days 15 hours 27m 13s, and is estimated to be a mere 20 million km from the surface of the primary.
Also, a phone call to the British Library has indicated that to their knowledge the only catalogues of Stars that appear in the library are those published in normal Astronomical publications aimed at amateur Astronomers or those in specialist publications aimed at the science community. The person I spoke to eventually had no knowledge of the publication of lists of stars named by private individuals, but she did add that that does not mean it was impossible, just unlikely.
To add to what Softus said, the two spellings of Rigel (Rigil) are from the arabic (Rijl) and the Latinised Greek (Rigil). The old Arabic spelling, Rijl, means foot. It can also be spelt Rij'al. Rigel had the name Ar-Rijl-al-gabbar in Babylonian which meant "The foot of the giant one". To the Babylonians what we call Orion was known as Anu, the Giant Shepherd of the sky.
After Johannes Bayer latinised things in the 17th century some Stars retained their designation, although some became abbreviated. Rij' al Anu would have meant the Foot of Anu (Shepherd of the Sky), but simply became Rigel, whilst Alpha Centauri, retained it's name of Rijl al Kentaurus (meaning Foot of the Centaur). This is also known as Tolliman, another Babylonian names meaning Ostriches!
Rigel also has some other oddities about it that make is stand out. Firstly, although designated as Beta Orionis (2nd brightest star in Orion), it is actually brighter than Betelgeuse (Alpha Orionis) as Bayer got this wrong, and Rigel is not a single star, but a triplet of B type supergiants and giants.