Health Monitor objects all use unique UUIDs when referenced internally by the system, so they will not interfere with each other even if a health monitor is created using the exact same name as a health monitor in another tenant.
However when creating a health monitor using Type = "External" where custom code is executed by the health monitor, this may interfere with an existing External Health Monitor if one is configured with the same exact name in another tenant.
This is due to a current limitation with Health Monitors of the type = External. Currently the custom code snippet entered by the user is saved into an internal file which uses the name of the health monitor as the filename
This will be fixed in future releases (31.1.x and 22.1.8), but the workaround is to use a unique name for the health monitor across tenants. As an example, you can append the tenant name when creating external health monitors (ie: oracledbcheck-finance)