Wow, I finally got back in the forum. I have had a terrible time trying to get in lately. Congratulations on getting the walnut and I look forward to seeing the projects from it.
The usual issue with leaving bark on is insect infestation. You didn’t mention whether it was sawed or still in the log but either way I would take the bark off. The only advantage would be to retard moisture loss in the round log which might help with checking some. You can run a cut to the heart of a log with a saw and can control the checking by giving the shrinkage a controlled relief in large logs. Logs normally loose most of their moisture through the ends and painting those can help equalize that and help prevent end checks. You want them to dry slowly but keeping them too moist will lead to mold and rot. I know of no advantage with leaving bark on sawed timber. If it is kept absolutely high and dry you can get away with it normally but there are no advantages and the insect issue in the worst case. I have seen old cabin logs with attached bark that have held up well (with the logs totally covered) but that was the exception and not the rule.
Just be sure to stack it well, providing support and ventilation, and preventing precipitation (metal roofs ) and roof leaks from getting to it.