val myLogging = log is ok as def log = akka.event.Logging(context.system, this) (simplified version) returns thread-safe LoggingAdapter because it's using asynchronous event bus provided from context.system (system.eventStream). The only non-thread-safe version of LoggingAdapter is this:
def apply(logSource: Actor): DiagnosticLoggingAdapter
as it's stated in API docs
Basically, you can create any logger you want as akka.event.Logging.apply is public.
P.S. Be aware that log will use your Actor's class for source name even if you pass it somewhere else.
P.S.2 You can also notice that def log = is already closed on your eventBus and actor (actor instance is used only for naming), so it might be even safe to call log.blabla directly from another thread. The only thing here it might cause reinitialization of _log as there is no double-checked locking. However, I'm not sure about some highly-optimized versions of JVM here - they might not follow "JavaMemoryModel" precisely especially when there is no @volatile annotation on _log.