In the maven-assembly-plugin you can add an optional parameter called appendAssemblyId (which is set to true by default) in the configuration tag of your assembly execution.
The use of this tag will generate two warnings indicating that you might override the main build of the artifact (done by the maven-jar-plugin).
If you don't want to override this jar with appendAssemblyId set to false, you can decide to build your assembly in another folder with the property outputDirectory.
Or the other solution if you are ok with the fact to have append something at the end of the name of your jar is to create your own assembly descriptor.
(for more information about the existing parameters or how to create your own assembly descriptor you can see the plugin documentation here : https://maven.apache.org/plugins/maven-assembly-plugin/assembly-mojo.html)
<plugin>
<artifactId>maven-assembly-plugin</artifactId>
<version>2.5.3</version>
<executions>
<execution>
<id>jar-with-dependencies</id>
<phase>package</phase>
<goals>
<goal>single</goal>
</goals>
<configuration>
<descriptorRefs>
<descriptorRef>jar-with-dependencies</descriptorRef>
</descriptorRefs>
<appendAssemblyId>false</appendAssemblyId>
<outputDirectory>${project.build.directory}/my-assembly/</outputDirectory>
</configuration>
</execution>
</executions>
</plugin>
Edit : I edited my answer in order to make it more complete.