The Java 9 module system (JSR-376) expects each JAR file to declare a module name. When building explicitly for Java 9+, the module.info file is used to define the imported and exported modules for a given JAR, but given that Tamaya targets JDK 1.8, the simplest way to define a module name for the released artifacts is to define an Automatic-Module-Name entry in each JAR's MANIFEST.MF file. Specifically, this would involve adding an appropriate line to the various bnd.bnd files in the code base.
In general, it seems that the defined module name would be the same as the OSGi exported module name: tamaya-core exports org.apache.tamaya.core via OSGi, so using the same (o.a.t.core) name would make the most sense.
The tamaya-api module, however, exports two modules: o.a.t and o.a.t.spi. I would suggest that tamaya-api's module name be: org.apache.tamaya.