You can, but the Leave Control Panel is not available through the “Customize Form” option in Setup, which means the safest way to add a new field there is with a custom app, or coding it and making a pull request on Github.
The Leave Control Panel itself is not a document that gets saved, instead it creates documents in bulk. There would be little point in adding a custom field there without modifying the tool’s server side code to push the new field to the created documents. I think that’s why it’s not made to easily accept a custom field.
So options are custom app, paid develoment job, or feature request on Github. Until the feature is there you CAN easily create a custom “Company” field in the Leave Allocation Form, just not the tool.