Asset Management for Jira ships with a Loanee field that lets you assign an asset to a Jira user.
We pre-populate this field with a list of all users on your instance - however, this is restricted to users with Atlassian accounts, since we can not fetch the customer account users.
To learn more about the differences between these two types of users, click here.
We recommend creating the users you want to assign as loanees with Atlassian accounts (this does not require them to have a Jira license). This also means you can sync them automatically via SAML.
If for some reason this isn't a viable option for you, you can set the value of the field manually.