The exporter collects metrics for a resource group. Different DB instances can be included into a same resource group. Exporter adds a label "resource_name" for identify different services.

Here is an example of monitoring resource group "pmmdemo" with two services
(PostgreSQL - pgadivinho, MySQL - pmmdemo-azuredb)
e.g.
cpu_percent_percent_average{
agent_id="/agent_id/e23750bd-fc0a-4cdd-a53c-004ee41dd2ac",
agent_type="external-exporter", external_group="external", instance="/agent_id/e23750bd-fc0a-4cdd-a53c-004ee41dd2ac",
job="external-exporter_agent_id_e23750bd-fc0a-4cdd-a53c-004ee41dd2ac_mr-10s", machine_id="/machine_id/ec2bacbc48a83a68b2929ad60b2841c7", node_id="/node_id/1bcf9f61-a0f9-4233-9473-dbcbecb676ca",
node_name="ip-10-178-1-239.us-east-2.compute.internal",
node_type="generic",
resource_group="pmmdemo",
resource_name="pgadivinho",
service_id="/service_id/86188215-4748-4ed8-8439-fc6168a12cd4", service_name="MyAzureDB",
service_type="external"}

cpu_percent_percent_average{
agent_id="/agent_id/e23750bd-fc0a-4cdd-a53c-004ee41dd2ac",
agent_type="external-exporter", external_group="external", instance="/agent_id/e23750bd-fc0a-4cdd-a53c-004ee41dd2ac",
job="external-exporter_agent_id_e23750bd-fc0a-4cdd-a53c-004ee41dd2ac_mr-10s", machine_id="/machine_id/ec2bacbc48a83a68b2929ad60b2841c7", node_id="/node_id/1bcf9f61-a0f9-4233-9473-dbcbecb676ca",
node_name="ip-10-178-1-239.us-east-2.compute.internal",
node_type="generic",
resource_group="pmmdemo",
resource_name="pmmdemo-azuredb",
service_id="/service_id/86188215-4748-4ed8-8439-fc6168a12cd4", service_name="MyAzureDB", service_type="external"}

Open

It's required to form a unique node_name for each service that would be based on resource group and name.
e.g.
pmmdemo-pgadivinho
pmmdemo-pmmdemo-azuredb