I wanted to know in royal families if a person carries I, II or III and so on would the person have the same name? (I mean like first, middle and last name.)

Yes - and they are not necessarily direct descendants. For example if a man's name is John Thomas Smith and his nephew is named John Thomas Smith, then the nephew would be John Thomas Smith II.

Well, the current Queen of England, Elizabeth II, has a full name of "Elizabeth Alexandra Mary" and I believe the last name would be Windsor (but the British contingent gets to correct me).

I can't find if Queen Elizabeth I had middle name (the evidence is that she did not), but she was the last of the Tudors and as near as I can tell, would have been called Elizabeth Tudor.

I may not have my act completely straight on this, but, my point is, I'm not so sure that the full names of persons I, II, III, etc. have to be the same. Certainly there are exceptions.

Thank You for clearing that up!

To add a few more details:

Elizabeth II (the Queen of England) is not a direct descendant of Elizabeth I, as Elizabeth I had no children. She is known as "the second" to differentiate her from the first Queen Elizabeth. Prince Charles does not currently use a number after his name, but if/when he becomes King, he would be known as Charles III if he decides to keep the "Charles" name (there have been two previous Kings named Charles). When crowned he has the opton of being known by a different name, and it has been suggested that he may decide to be known as George VII.

This is how an ignorant Yank like me understands it - perhaps one of our British friends will correct me if I'm in error.

As Kings and Queens are known by the first name the numbers are used to differentiate between them, so NO it's not the complete name that's the same.

As for PRINCE Charles, as he isn't King, and may not be anyway, he doesn't use a number.
Technically as he has married a divorcée he cannot be King due to English Constitutional Law.
This has happened previously: Edward VIII of the United Kingdom - Wikipedia, the free encyclopedia