The Homeric name Πενθεσίλεια seems to come from πένθος "grief" and λαός "people", presumably meaning something like "grieved by the people". This would be drawing a parallel to Ἀχιλλεύς, if that name really comes from ἄχος and λαός ("pain of the people"), as some ancient authors speculated.
But it's not clear to me how this compound is formed. The first part looks like a dative plural (uncommon but not unheard of in Homeric compounds, like Ναυσι-κάα), but I'm not sure what it would mean for this abstract noun to be plural, or why it would be dative in this instance.
Why is πένθεσι dative plural—or, why does it have this form if it's not dative plural? How is it supposed to be connected to λαός here?
EDIT: Nagy also brings up Πρωτεσι-λαος and Χαιρεσι-λαος, which show the same suffix on their first component, but I remain unclear what exactly that suffix is. The latter suggests it might be a verb ending—TKR in the comments mentions πενθέω—because there's χαιρέω but no *χαίρος that I know of…but I'm not aware of a verb or noun that could supply the first one.