King Oberon is your grandfather, of course. Make sure you treat him with the respect he deserves. He's banned his children from procreating, so he's not going to be pleased to see you. But if you keep your head down, I'm sure he'll come around. Just don't anger him, whatever you do. His torture chamber is very well used.
You'll meet Prince Eric soon enough. He claims to be the Crown Prince, although his father his never declared it to be so. He has a reputation as a lady's man, although I honestly don't know why.
Prince Caine is second in line for the throne, although he certainly doesn't take himself so seriously. Amongst the commoners, he's the most respected of the Royal Family. He worked his way to the rank of Admiral in Amber's Fleet. He's a man of his word, and his word is Amber.
Prince Bleys and Prince Brand are the only full brothers remaining in the family. You'll know them when you see them; they both have shockingly red hair. In temperment, however, they couldn't be more different. Prince Bleys is the life of every party, as quick with his wit as he is with his sword. Prince Brand is soft-spoken and reserved, and a nicer man you would never find. Of the two, I believe Prince Brand is the more popular - although I certainly wouldn't tell Bleys that!
That is all of the family you will find in Amber these days. Princes Benedict, Gerard, and Julian have been in Shadow for some time, now. I have no doubt they will return when they tire of their exploits, and yearn for the solidity of Amber once more. And Corwin, Eric's full brother, has been dead these four hundred years.
Ah, you have heard of Prince Random? Yes, most people have. He, of course, is the reason that King Oberon has banned his children from procreating. I'm sure you've heard the stories, but I will rehash the scandal once more. Prince Random did, indeed, father a child to a princess of Rebma. And when he denied paternity, the princess in question was so heartbroken that she took her own life. Now, Prince Random's son lies in Rebma, unwanted and unnamed. And Prince Random himself has fled into Shadow, determined to avoid his father's wrath.
That is the entirety of your new family, your Highness. Oh yes, there are the Princesses. I always forget about them. Princesses Dierdre, Fiona, and Florimel can be found wandering around the castle grounds, or sewing within their rooms. King Oberon does not encourage them to become involved with matters of state, or anything more complicated than cross-stitch. It is well known that too much thought addles a woman's brain, and reduces her beauty.
Ah, here are your rooms, your Highness. I hope you have a pleasant day. If you have any questions, please don't hesitate to ask.