In the Library modules right panel, the Metadata section has a limited variety of metadata groupings to select from for display where data can be updated directly after Import, Video in not there by default. But the presets that can be applied in that panel to a file, include the video group, which has Shoot Name in it.
1. You can use a preset to update Shoot Name after Import.
2. If you create a preset that has data in the Video section, the Video group is added to the drop-down list and any of its continence, including Shoot Name, can then be made visible in the Metadata section of the Library panel and can be used to update selected images in Grid mode without requiring a preset.
There still is a problem. The Text Filter for “Any Searchable field” will not pick it up.