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There is no Icelandair name change fee, if you request a name correction within 24 hours of booking. But after the 24 hour risk-free period, if you make any corrections to your name, you will be responsible for the name change fee. The name correction fee varies based on your correction type.
https://sites.google.com/view/....icelandair-name-chan

Icelandair Name Correction Policy

Icelandair Name Change Rule
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