Not really. There isn’t an admin-managed concept like “Serverless Cluster A for Team A” and “Serverless Cluster B for Team B” for notebooks/jobs serverless.

Serverless compute is described as Databricks-managed on-demand resources where Databricks “automatically allocates and manages the necessary compute resources” instead of you provisioning/creating clusters.

If it is for cost tracking. Databricks provides Serverless budget policies (public preview) that apply tags to serverless activity for users/groups assigned to those policies. Those tags then appear in billing records, enabling chargeback/showback by team/cost center.
https://docs.databricks.com/aws/en/admin/usage/budget-policies