When starting a new game with the default asteroid configuration, the first asteroid is always named HSJ-227, and is always placed into the following orbit:

ORBIT
{
    SMA = 30538612101.3155
    ECC = 0.136886541924265
    INC = 6.05229021995948
    LPE = 146.525451660156
    LAN = 156.887023925781
    MNA = 278.716278076172
    EPH = 0.04
    REF = 0
}

I believe this is a problem with KSP's stock random number generator, so it may not be worth the trouble of working around.

Update May 10: the issue has now spread to standardizing the first two asteroids that are spawned.