I've never rebuilt an EOS, but I've rebuilt a fair number of regs now, and heard a lot of different sounds. One sound is a diaphragm rattle when you breathe in on the second stage above water. This, to me, can sound like a moose in heat. This sound should go away underwater. It's caused by a harmonic between the diaphragm and the demand lever and can be exacerbated by slop between the lever and the diaphragm.
A second moose-like sound can be caused on the exhalation by the exhaust valve(s). Again, this is just rattling and should go away under water.
A third sound, and one that is unique to DVT first stages like the EOS, is caused by the DVT system. When you first pressurize a DVT first stage, there is a huge pressure imbalance across the red DVT plug. This imbalance causes the plug to open and allows air to flow into the first stage from the tank. When the first stage locks up, the DVT plug closes up. It stays this way until you take a breath off the second stage. Once again, there is a pressure differential across the plug which forces the plug to open. The restricted opening in the intake causes air to hiss by the plug, and you can hear that. The restriction also makes the first stage slower to re-achieve lockup pressure, so the hiss continues for a second or so after you quit inhaling. I've had customers ask about the funny noise their reg makes underwater and I can duplicate it on the flow bench. I've had one customer request I take the DVT plug out of the reg, which I did. The noise went away. I think this noise is just the price one pays for having the DVT system on his reg. I've heard this noise off many Oceanic and Aeris regs, and I've seen a few DVT regs that don't make the noise at all. I'm not sure why some do and some don't.
None of these noises should be dangerous and you're not doing anything wrong. Just to be safe, though, if I were you I'd take my reg to the shop and verify with the service tech that the sound is benign and not indicative of something worse.
Hope this answers your question.