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?