In order to configure the file name of the generated report (which is "surefire-report" by default), the outputName property should be set to its new name.
<project>
[...]
<reporting>
<plugins>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-surefire-report-plugin</artifactId>
<version>2.15</version>
<configuration>
<outputName>newname</outputName>
</configuration>
</plugin>
</plugins>
</reporting>
[...]
</project>
And after executing the mvn site, the generated report file is named to newname.html.