Enfin and finalement are very close to each other. There's a slight difference in usage but, as I understand it, it is very slight.

Enfin -- in the end, at the end of of the day.

Also used as a single word exclamation for -

at last!

Finalement -- finally

If you want a more scientific dissection of their similarities and differences, look no further:

https://journals.openedition.org/praxematique/3919?lang=en