The latest Shonen Jump issue reveals Velvet's full name as Velvet Crowe.
Velvet's full name is Velvet Crowe (ベルベット・クラウ, berubetto kurau, romanization official from newer news sources). The scan also has character illustration for Laphicet (Special thanks to @kazu4281 for the scan.)
The scan gives us a bit of info on Velvet's background. One night, when the moon was red, a tragedy occurred - Velvet lost her beloved family. Jump 3 years later - one can see in Velvet's eyes that she is still full of rage for the one who stole everything from her.
As for Laphicet, his quote is "After all, isn't it hard to suffer alone?"
It is mentioned that his race is that of a "spirit" ( 聖隷, seirei). In this world, humans apparently use "spirits" as slaves (which might explain the collar-like accessory around his neck). Though Velvet initially scolds him for his lack of initiative, he eventually becomes a source of support for her.
In addition, the compass that Lifiset holds will be a key part of the story. Where it points will help his mind and heart grow.
Many thanks to @Otsukareia for the translations!