During the Muslim period, there were several courts and capitals in different regions and dynasties. The specific name of the court and capital would depend on the time period and the ruling dynasty. Here are a few examples:
Delhi Sultanate: The Delhi Sultanate had multiple dynasties and, as a result, multiple courts and capitals. The most famous among them is the Qutb complex in Delhi during the Mamluk and Khalji dynasties. Later, during the Tughlaq dynasty, the city of Tughlaqabad was established as the capital.
Mughal Empire: The Mughal Empire had its capital in various cities, including Agra and Fatehpur Sikri, but it is most famously associated with the Red Fort in Old Delhi (Shahjahanabad) during the reign of Emperor Shah Jahan.
Abbasid Caliphate: The Abbasid Caliphate, which was based in Baghdad, had its own court in the capital city of Baghdad.
Ottoman Empire: The Ottoman Empire had its court in Istanbul (formerly Constantinople) at the Topkapi Palace and later the Dolmabahçe Palace.
Safavid Empire: The Safavid Empire had its capital in Isfahan, where the Shah's court was held at the Chahar Bagh complex.
These are just a few examples, and there were many other courts and capitals during the various periods of Islamic history. The names and locations of these courts can vary depending on the time and place within the broader Muslim period.