Doh, it's right there isn't it - the gliese number on the NSL!
So in the interests of completeness, and using the handy
ARICNS Gliese database, here's the other named stars in 2300AD identified... Where I can I've listed HIP numbers so you can find them in Celestia too.
Augereau is Gliese 412 (aka Lalande 21258, HIP 54211, companion star to WX Ursae Majoris (variable star))
Botany Bay is Gliese 638 (aka HIP 151288, SAO 65525)
Berthier is Gliese 438.1. This is now known to not actually be a nearby K2 V at all, it's a K4 III giant over 1000 ly from Sol.
Bessieres is Gliese 411 (HIP 54035, Lalande 21185.
This is known to have a planetary system)!
Broward is Gliese 628 (HIP 80824, Wolf 1061, V2306 Ophiuchi, variable/binary?)
Clarke's Star is Gliese 644 (aka HIP 82817, Wolf 630). Triple star system.
D'Artagnon is Gliese 693 (Luyten 205-128, HIP 86990)
Davout is Gliese 682 (HIP 86214)
Ellis is Gliese 623 (HIP 80346). This star is
known to have a companion that is right on the border between red and brown dwarfs, at about 80 jupiter masses).
Haifeng is Gliese 83.1 (though the spectral type is wrong, it should be M4.5 V) (HIP 350010, Luyten 1159-16, TZ Arietis)
Hochbaden is Gliese 528 (HIP 67422, HD 120476)
Hunjiang is Gliese 1 (HIP 439, HD 225213, Cordoba 32416, LHS 1)
Kimanjaro is Gliese 480.2 (HIP 61887, HD 110296). This turns out to be incorrect in Gliese 2, it's actually about 870 ly from Sol. Ooops).
King is Gliese 673 (aka HD 157881, HIP 85295, BD +02 3312, or LHS 447)
Neubayern is Gliese 380 (aka HD 88230, HIP 49908, BD +50 1725, or LHS 280).
New Melbourne is Gliese 686 (HIP 86287)
Nyotekundu is Gliese 406 (aka Wolf 359/CN Leonis)
Qinyuan is Gliese 65 (Luyten 726-8, HIP 350002, companion to
UV Ceti)
Red Speck is Gliese 661 (BD+45 2505)
Serurier is Gliese 729 (Ross 154, HIP 92403, V1216 Sagitarii). Known to be a flare star.
Vogelheim is Gliese 484.1 (HIP 62386, HD 111180). This is actually 945 lightyears away.
Xiuning is Gliese 832 (Luyten 354-89, HIP 106440, HD 204961)
Oh, and Gliese 229, which was the first star to have a Brown Dwarf in orbit around it, is listed as DM-21 1377 in the NSL.