Once, when telephoning the international PR office of a major electronics manufacturer, I got lucky. Without my even asking, the young woman who picked up the phone volunteered her name, saying 私は青木と申します (Watashi wa Aoki to mōshimasu, My name is Aoki). Actually it sounded more like ア・オ・キ (Ah-Oh-Ki), which she stated as three clearly enunciated syllables, almost musically varying her pitch.
Ms. Aoki knew that via telephone, when a non-native speaker of her language can't make eye contact or exchange business cards, the foreign ear appreciates a little help, and she made an extra effort to pronounce her name clearly from the start without sounding the least bit patronizing. I immediately sensed she was a skilled communicator and our subsequent dealings confirmed that to be the case.
Experience will show that asking people's names — which is done in polite speech by asking お名前はなんとおっしゃいますか (onamae wa nan to osshaimasu ka, how do you say your honorable name?) — can generate unpredictable responses, because Japan is estimated to have up to 300,000 surnames. Truly one could say, 日本の名字はバラエティに飛んでる (Nihon no myōji wa, baraetii ni tonde iru, Japan has a cornucopia of surnames).