The objective of this process is to mark the application as Managed, assign a Business owner, and add license and renewal data.
If you're researching a new application it's often useful to understand who is actually using it. To help get context, it's a good idea to add the Job title and Team columns to the Users tab:
User list for an application, showing "Job title" and "Team" fields
Another useful tool is the Insights tab - choose Team engagement to see a breakdown of users by team. This only works if you have teams data being supplied by your Identity Provider or HR system.
A good way to identify business owners is to use the Similar apps panel on the application profile page. Find other apps that are similar but already Managed with assigned Business owners. These people will likely want to be aware of similar sorts of application in use and will likely be able to help you understand more about why a related application is being used.
Looking at related applications
Mark the application as Managed and assign a Business owner, and contact them to add relevant license and renewal information.
Alternative ways forward are deciding that the application does not need formal management and mark it as Accepted or if usage seems inappropriate, mark as Plan to close.