Wemmick calls his home The Castle because a man’s home is his castle, and his has some added features that make it castle-like.
Jaggers’s clerk Wemmick makes a point to keep his private life separate from his work life.
No; the office is one thing, and private life is another. When I go into the office, I leave the Castle behind me, and when I come into the Castle, I leave the office behind me. (ch 25, p. 142)
At work, he is surrounded by the “cobwebs” of Newgate prisons and the criminal classes. At home, he is surrounded by people who love him. He has his Aged, his father, and Miss Skiffins, his girlfriend.
To keep home whimsical and please his father, Wemmick has decorated the house to look like a castle.
Wemmick's house was a little wooden cottage in the midst of plots of garden, and the top of it was cut out and painted like a battery mounted with guns. (ch 25, p. 141)
The guns actually fire! Wemmick says it is one of the few sounds his deaf father can hear, and it makes him very happy.
The contrast between Wemmick’s home life and his work life is a real surprise to Pip. When Wemmick brings him home, Pip sees another side to him. He realizes that Wemmick is actually a kind and gentle soul, and he is able to get enjoyment out of life. At this point, Wemmick is one of Pip’s only positive role models. He is learning what is really important.
The castle is the suburban home of Mr. Wemmick and his Aged Parent. It is described in detail in chapters 36 and 37 (see link below). Wemmick, Mr. Jaggers assistant, has built his home himself and designed it to look like a miniature castle complete with a moat and a little drawbridge. Everything is miniaturized. Wemmick invites Pip there and shows himself to be a completely different person when he is at home than when he is working in the law office in London. Wemmick proves to be a kindly man, devoted to his father, who is completely deaf and senile. Wemmick is also an eccentric individual with fanciful habits, such as firing a little cannon once every evening, to the delight of Aged Parent. Pip meets a Miss Skiffins, Wemmick's fiancee, at the castle and later attends their wedding. The visit to the castle serves no particular plot purpose except to strengthen the relationship between Pip and Wemmick, who will prove a good friend to Pip when Magwitch reappears in England. Wemmick has a sentimental side which distinguishes him from his employer Jaggers. Wemmick is willing to be more helpful to Pip than Jaggers, who is noteworthy for his cautious adherence to the exact letter of the law.