Seems you can't do this natively with Azure Monitor default metrics that I see. You can however, do this with telegraf via procstat plugin. https://github.com/influxdata/telegraf/blob/master/plugins/inputs/procstat/README.md .... I won't explain how to setup telegraf as there is already guides out there but if its setup properly and you do this, it'll be working.
I configured it like so
Monitor process cpu and memory usage
[[inputs.procstat]]
Must specify one of: pid_file, exe, or pattern
PID file to monitor process
pid_file = "/var/run/nginx.pid"
executable name (ie, pgrep <exe>)
exe = "nginx"
pattern as argument for pgrep (ie, pgrep -f <pattern>)
pattern = "nginx"
exe = "grafana"
Field name prefix
prefix = "grafana"
add name of process to monitor... such as below omiagent
[[inputs.procstat]]
exe = "omiagent"
prefix = "omiagent"
This now shows omi agent cpu_usage data for that process which I can now monitor and set alerts for specific thresholds
