Use exec -a to differentiate app and probe process names.

docker/Dockerfile

@@ -3,7 +3,7 @@ MAINTAINER Weaveworks Inc <[email protected]>
 LABEL works.weave.role=system
 WORKDIR /home/weave
 RUN echo "http://dl-4.alpinelinux.org/alpine/edge/testing" >>/etc/apk/repositories && \
-	apk add --update runit conntrack-tools iproute2 util-linux curl && \
+	apk add --update bash runit conntrack-tools iproute2 util-linux curl && \
 	rm -rf /var/cache/apk/*
 ADD ./docker.tgz /
 ADD ./weave /usr/bin/

docker/run-app

@@ -1,3 +1,3 @@
-#!/bin/sh
+#!/bin/bash
 
-exec /home/weave/scope app $(cat /etc/weave/scope-app.args)
+exec -a scope-app /home/weave/scope app $(cat /etc/weave/scope-app.args)

docker/run-probe

@@ -1,3 +1,3 @@
-#!/bin/sh
+#!/bin/bash
 
-exec /home/weave/scope probe $(cat /etc/weave/scope-probe.args) $(cat /etc/weave/apps)
+exec -a scope-probe /home/weave/scope probe $(cat /etc/weave/scope-probe.args) $(cat /etc/weave/apps)