"May I know who you are?"
Translation:Puis-je savoir qui vous êtes ?
so in french, in a question, we only switch the subject of the sentence (Je, in this case) with the main verb (Puis, (pouvoir)) and the rest of the sentence is the complement.
The sentence in a neutral form would be like:
Je / peux / savoir qui vous êtes
Subject / verb / complement
The sentence in a question form is:
Puis- / je / savoir qui vous êtes
Verb / subject / complement
Connaître means more along the lines of personally knowing someone/something, vs savior which is to know of someone or something.
Here is a helpful article on the difference: https://www.frenchtoday.com/blog/french-vocabulary/savoir-versus-connaitre-the-verb-to-know-in-french