The eldest daughter of King Lear. Cordelia is the only one of Lear's girls who isn't willing to suck up to her father for the sake of her inheritance. When the old man asks her how much she loves him, instead of gushing and stroking his ego, she tells the truth, I love you as much as a daughter should love her father. Lear gets pissed and sends her away. Meanwhile her sisters Regan and Goneril, dispite their proclaimations of love for Lear, secretly plot againt him.

In addition to the eldest daughter of King Lear:

Cordelia Gallowglass

Third child (and eldest daughter) of Rodney d'Armand and Gwendylon Gallowglass in the The Warlock series by Christopher Stasheff

Cordelia Naismith Vorkosigan

Mother of Miles Vorkosigan in the series of that name by Lois McMaster Bujold

Cordelia Chase

Character played by Charisma Carpenter on the WB TV shows Buffy and Angel, written by Joss Whedon.

Cordelia Ransom

Evil demagogue in the Honor Harrington series by David Weber

A satellite of Uranus

Discovered in 1986

Anne of Green Gables

What she wanted to be called ("Lady Cordelia de Montmorency, abducted by gypsies when (she) was three"), before settling for Anne-with-an-E. -Thanks to Gritchka and caknuck

Me

No, my real name isn't Cordelia. (In fact, my name is cordelia, not Cordelia. The story can be found on my homenode.

Discovered by            R. Terrile
Date of Discovery        1986
Distance from Uranus     49,770 km
Radius                   13 km
Mass                     ???
Orbital Eccentricity     0.00026
Orbital Inclination      0.08°
Orbital Period           0.3350338 day
Rotational Period        ???
Density (gm/cm3)         ???

Tiny Cordelia serves as the inner shepherd moon for Uranus's epsilon ring. It is also Uranus's innermost known moon. Discovered by means of imagery from Voyager 2, this moon was instrumental, along with Ophelia, in the development of the theory of shepherding. Not much else is known about it.

Sources:
NASA.gov
space.com