There are many different ways to spell the anglicised versions of Thai words; in this case Buakhao is actually two words, spelt 'Bua khao' or sometimes 'Bua khaw' (and no doubt sometimes another spelling). This means 'white lotus' or 'Water lily flower'. I can't find an authrative online source for that, except that it's part of the name of a Thai kickboxer and he does have a wiki page!
'Soi' is the Thai word for a street that runs off a main road.
Therefore Soi Bua Khao means "White Lotus Road".