I've had my 338-06 almost 20 years,and I have never shot anything but necked-up 30-06 brass. No problems, no issues and I've shot some fairly hot loads out of mine. The headstamp doesn't matter. Confusing a loaded 338-06 for a loaded 30-06 MIGHT be a problem but you can actually see the size difference between the two. That is assuming that you also have a 30-06, if not then you have no problems at all

Brass with a 30-06 headstamp is both cheap and easy to find. Good Luck.