My question is: What is the ruling on naming a newborn girl Haseebah? May Allah grant you success.

The default rule for naming is permissibility, unless there is a Sharia-prohibited element, such as servitude to a creature, or if the name is丑陋 (ugly), or involves imitation of polytheists, or contains dispraise or exaggerated praise. There is no objection to naming a newborn "Haseebah." However, it is preferable to name children with names encouraged by Sharia, or the names of prophets and righteous people.