[ajmurmann]

"For a bilingual child it's much more important for the name to sound the same that to be written the same."

This feels like it will be annoying whenever someone asks for your name in order to write it down or when they are trying to read it. This happens a lot in a school context.

[OJFord]

You're only at school in one of the countries (at a time anyway) - pick the one that corresponds there?

Of course only one of them is your 'actual' name anyway, the other is just by its existence making your name familiar and easy to pronounce. It having a different local spelling (if that's the case) doesn't have to matter or be annoying unless you decide it is. Anything where it's important obviously you make sure to get it right, as you would anyway.