After adding a new company (Manage > Assets > Organizational Types > Company), it saves but after the list is refreshed, it does not appear.
This is working as designed. The new company name used matched a wildcard in Software Management's Known-As function. This automatically merged the new company name with an existing company name to avoid duplication. The new company name still exists, but only now as an alias to the actual company name.
If it is not desired to have new company names merge with an existing company name, change or remove the wildcards that are configured for the existing company name in Software Management's Known-As function. This is found by going to Settings > All Settings > Software > Software Catalog and Software Library. WARNING: It is not recommend to change or remove wildcards for existing company names. This is because this information ties heavily into Asset Management and Inventory Solution for Software License Compliance. Changing how this works at this level can negatively impact this, therefore.
A workaround is to name the new company something other than what a wildcard will merge with. For example, "MSoft" could be used for "Microsoft" to avoid being merged.