General Notes

Berchan's Prophecy, stanzas 181-182 (as quoted in A.O. Anderson,Early Sources of Scottish History, vol. I, p. 574) says thisabout Malcolm II, son of Kenneth: Son of a woman of Leinster ...A son of the cow that grazes upon the country-side of Liffey,... This seems to indicate that Malcolm II's mother, the queenof Kenneth II, was Irish, and it ought to be possible to connecther to the royal genealogies of Leinster. But how?
Sorry to disappoint you, but this is all that is known of her.No contemporary record which names her.  She was probablyconnected with the Leinster royal family, but because there wereso many branches of it, it is unlikely.  The available Scottishand Irish Annals have been poured over with a fine tooth comb,and unless new records are discovered, which is not likely, weknow all that we ever will.
Not that I believe everything in Mary Elizabeth Cumming Bruce,Family
Records of the Bruces and the Cumyns (Edinburgh, 1870), but shesays, pp. 9-10: "Kenneth, brother of Duff, next succeeded [971].They were both sons of Malcolm I. Kenneth . . . did homage toEdgar [King of England] for Cumberland and Westmoreland. He alsodefeated the Danes. Kenneth married a daughter of WilliamLong-epee, Duke of Normandy, by whom he had Malcolm II andDunclina, who married Kenneth, Thane of Lochaber, and was motherof Bancho. . . . [994] Kenneth was assassinated at Fettercairnby the Lady Fenella, whose son he caused to be put to
death."
So possibly the Norman records would yield a name.  I've never
followed up this claim.