A 1901 Map (UK National Archive ref: CO 700-Hong Kong and China22) shows Kowloon Hotel on Elgin Road (today's Haiphong Road), roughly where the junction of Hankow Road is today. The lot is shown as IL 410.
Notification 453 in the 1893 Government Gazette shows it was previously called the Kowloon Club, but became the Kowloon Hotel in late 1893 / early 1894:
Special Sessions of Her Majesty's Justices of the Peace will be held in the Justices' Room, at the Magistracy, on Tuesday, the 19th day of December, A.D. 1893, at Eleven o'clock in the forenoon, for the purpose of considering an application from one L.M.Lobo for the transfer of the Publican's licence now held by him for the sale of intoxicating liquors in the premises known as the "Kowloon Hotel" situate in Robinson Road, Tsim-tsa-tsui, to the premises known as the "Kowloon Club" situated in Elgin Road, Inland Lots Numbers 409, 410 and 411, Tsim-tsa-tsui.
H. E. Woodhouse,
Magistracy, Hong Kong, 8 December, 1893.