[subject] + 姓 + [surname] 您贵姓?
姓 is a verb meaning "to have the surname". The surname follows it directly.
wǒ我de的xìng姓shì是Wáng王 is not how this is said, and neither is wǒ我shì是xìng姓Wáng王.A Chinese name puts the family name in front: 王明 is Mr Wang, not Mr Ming. The same big-to-small ordering governs dates and addresses.
Literally "your honourable surname". The answer drops 贵 and usually adds the given name.
Answering 您贵姓 with 我贵姓林 is wrong – 贵 is a courtesy directed at the other person.
姓 takes only a surname, 叫 takes a given name or a full name.
It also means "surname" as a word: 中国人最常见的姓.
王老师, 李阿姨, 周经理 – the surname comes first and the title follows.