There won't be a problem. The NHS app isn't intended to be your surrogate passport, it simply proves that you - and no-one else - had the specified vaccinations. I imagine the date of birth is correct throughout, for example. Now it's not surprising that the offline checks fail given the name imbalance, but at the airport if they check this - which I doubt - then they'll still clear you. Just calmly present documentation as required and when asked at check-in. Incidentally my NHS name doesn't align with my passport either, it isn't unusual, never mind all the maiden versus married name mis-matches. The sky won't fall in.