Names That Mean Princess

Less well known internationally than Saoirse, but equally appealing, this Irish name is also spelled Saorla or Saorlaith.

Saorfhlaith

Zippy and multicultural, Sarika can be considered a pretty nature name, referring to a myna bird in Hindi and Sanskrit and to a blackbird in Khmer (or Cambodian). In these contexts, it would be pronounced as SAHR-ka (Sanskrit) and  saw-ree-GAW (Khmer).
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Alternatively, it can be used as a form of Sarah, notably in Hungary, though the spelling Sárika is typically preferred, but also in Spain, Bosnia, and Croatia. In Hungarian, it is pronounced as SHA-ree-kaw, while in Spanish (and likely in English), it is said as sa-REE-ka, and in Bosnian, it is said as SAH-rih-ka.
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The Indian actress Sarika Thakur, known mononymously as Sarika, is a notable bearer.