What is the name of this mountain/hill chain, northwest of Secomber? I can't seem to find any information on them, much less their name.
Map excerpt from free map of NW Faerûn published by WotC
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Scourge of the Sword Coast includes a detailed (and well labelled) map of the area - which tells us the hills in question are called The Forlorn Hills.
A less detailed, but still well-labelled, map can be seen at the Forgotten Realms Wiki.
And another can be found in the pages of the free Web Enhancement download for City of Splendors: Waterdeep.
As other users said, they're the Forlorn Hills, while Marco Volo also states:
Well-learned folk know the [Crumbling] Stair to be a ruin that stands in what some call "the Sword Hills," a lawless, brigand-infested hill country east of Waterdeep, betwixt Ardeep Forest and Uluvin
This is in "The Adventures of Volo - the Crumbling Stair" by Ed Greenwood, I believe it's in Dragon #275.