A professional private investigator can definitely find someone online. But there is a lot more to the process than just typing a name into a search engine. Investigators use both digital technologies and real investigative methods to put together a reliable profile of the individual they are looking for. This is different from regular searches.
Finding someone whose current whereabouts is unclear is called skip tracing. Skip means someone who fled suddenly, and "trace" means finding them using information and investigation procedures that are already available.
You're also trying to find solid proof of behavior that supports or refutes your suspicions. Investigators use a number of different methods to put together a clear picture.
Survellience is not about tracking the subject with binoculars. Professional Surveillance investigator services have the skill of tracking the culprit both digitally and physically.