Got SE key, but not sure should I register now?

I got the full SE key for Heavensward, but my mogstation account did not display my main character name, only 3 alt chars shown in my mogstation acc, I have total 4 char names inside. As SE mention in Lodestone:

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We have begun fixing the issue causing certain character information to not display correctly on The Lodestone, the FINAL FANTASY XIV Forums, and the Mog Station.

The issue causing a character’s World information to not be displayed correctly is still being investigated.

We will provide more information as it becomes available and apologise for any inconvenience this may cause.

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Should I register the HW code or should I wait?

The HW code works on your entire account not just a single character therefore you should be okay to register it.

I see, its odd that my main character name disappear in my mog acc. I'll register it and hope there won't be a problem.

character name only disappeared cause of problem with mogstation which they are still fixing.

go ahead and do it now since it works on account just login to mogstation and register it and u should get items in 20mins or so when game is officially launched for expansion