誕生日を祝ってくれてありがとうって英語でなんて言うの？

"Thank you for remembering my Birthday!"
Use this expression to thank someone for giving you a gift or card for your Birthday.
Remembering - Doing something, like giving a gift to show that you did not forget someone's Birthday.

"Thank you for celebrating my Birthday with me!"
This expression is useful for thanking someone for coming to a Birthday party or dinner. You are thanking them for coming and spending time with you.

It's especially nice to be remembered, so thanking someone for 'remembering' is a sincere and kind way of expressing this. We can also say we 'appreciate' something or someone as a way of expressing gratitude.

appreciate/appreciation is a term used when you are thankful, understanding and the acknowledgement of something.
it shows someone cares when they make the effort and remember and celebrate your birthday.

If you have completed an activity for your birthday, such as a party or outing, then you can thank someone for coming using these expressions. If they have simply wished you a happy birthday or bought you a card or gift then you can thank them for these, for example, 'thanks for remembering my birthday' or 'thanks so much for the present and card!' You can also use phrases like, 'I really appreciate it' to show even more gratitude.

Grateful is another word for thankful
To appreciate something is to be glad it was done

Saying "you remembered" is a great way to show that you appreciate the fact that they went out of their way to wish you a happy birthday.
Saying "so much" can emphasize your gratitude.