The most obvious one in recent memory is Cordelia Chase, in both Buffy the Vampire Slayer and its spinoff Angel, as played by Charisma Carpenter.
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The show Blue's Clues had a character named Blue.
90210 has a character named Liam.
The Jingles Show (or Jingles of Boofland)
The Beverly Hillbillies
the Mod Squad