お名前を伺ってもよろしいですか

The phrase is a combination of several polite linguistic elements in Japanese. 'お' (o-) is an honorific prefix, indicating respect for the person or thing being referred to. '名前' (namae) means 'name'. 'を' (o) is a direct object particle. '伺っても' (ukagatte mo) is the te-form of '伺う' (ukagau), which is a humble verb meaning 'to ask' or 'to inquire', used when referring to one's own action of asking someone of higher status. The '-te mo yoroshii desu ka' (〜てもよろしいですか) is a highly polite and formal construction used to ask for permission or to make a polite request, essentially meaning 'Is it alright if I (do something)?'. The 'desu ka' (ですか) at the end turns the statement into a question. The overall construction reflects the intricate system of honorifics and humble language (keigo) in Japanese, which emphasizes social hierarchy and mutual respect. This particular phrasing is suitable for formal situations or when speaking to someone of higher social standing, age, or a client, demonstrating utmost deference.