"What's your name?" <- most common "Can I ask your name please?" <-uncommon/polite "Could I ask your name?" <-common/polite

'Could' as opposed to 'can' - like 'would' as opposed to 'will' - has the effect of 'distancing' the speaker from the situation. It makes you appear more tentative, and therefore more polite. 'Will' and 'can' are quite direct, whereas 'would' and 'could' suggest a more hypothetical possibility. So, yes, in most business situations it would be better to use 'could' and 'would'. English doesn't have anything the same systems of formality and hierarchy that Japanese does, but this use of conditional-style modal verbs is certainly one way of appearing more polite and respectful to someone.

Thank you!

Could I ask your name?- is really polite