Because Prince Charles was - and still is - the Prince of Wales
when she married him.
Her name was never Princess Diana. He correct title was Diana,
Princess of Wales.
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Princess of Wales Hospital was created in 1985.
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Princess of Wales Bridge was created in 1992.
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No she was not the first Princess of Wales. The title Prince of
Wales was established in 1307 by Edward I. There have been 10
Princesses of Wales since it was established and Diana was the
9th.
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Princess of Wales's Royal Regiment was created in 1992.