By incident we noticed that when replacing a master with a different one (in turn this means we moved the local .jenkins folder on the slave), the Jenkins master creates a new (second!) windows service.

This is rather untypical on Windows. A service is typically serving all instances at once, the idea of one service per instance is untypical.

To sum up, it would be great if the service would simply be called "Jenkins", and serve both folders.

A second service would only be needed in case the two masters want to run different user accounts. In that case, it makes more sense to name the Jenkins slave services not by installation folder but by master's host name.

Or even better, provide a "CI domain name" to the master, and use that one.