Hi
No - there is no companion Health app on Apple Watch.
Instead, the Heath app on your iPhone receives and combines health and fitness data from Apple Watch, iPhone and any other data sources. When reporting the combined data, the Health app adjusts results to avoid any double counting of data from different sources:
iPhone also includes a companion Activity app, where you review historic Activity data from your Apple Watch, including Workout summaries:
Use the Activity app on your Apple Watch - Apple Support
More information:
Use the Health app on your iPhone or iPod touch - Apple Support
Manage Health data from multiple sources on your iPhone, iPod touch, or Apple Watch - Apple Support