From a South Asian royal title, raja, meaning king or prince.
Rajah derives from the Sanskrit word "raja" (राजा), meaning king or ruler — one of the oldest and most geographically widespread royal titles in the world. Sanskrit itself is among the oldest attested members of the Indo-European language family, and "raja" shares a distant etymological ancestor with the Latin "rex" and the Celtic "rix" (as in Vercingetorix), all descending from a Proto-Indo-European root meaning to govern or straighten. When you name a child Rajah, you are invoking a title that has been used from the subcontinent to the Indonesian archipelago for more than three thousand years.
Rajas governed kingdoms large and small across South Asia for millennia, and the title spread outward with Hindu and Buddhist cultural influence into Southeast Asia — the Malay peninsula, Java, Bali, the Philippines. The English loanword "rajah" entered the language through colonial contact in India and remains in standard English dictionaries. James Brooke, the first White Rajah of Sarawak in nineteenth-century Borneo, made the title especially exotic and romantic to Victorian readers; Rudyard Kipling and other writers of the period threaded rajah-imagery through their work, cementing the word's association with jungle kingdoms and imperial adventure.
As a given name in the modern era, Rajah is used in South Asian and Southeast Asian communities as a direct invocation of its kingly meaning — an aspirational name expressing the hope that a child will carry himself with dignity and authority. It has also been adopted more broadly in the United States and the United Kingdom, where its exotic register and strong sound give it appeal across cultural boundaries.