Gimli is only saying poetically that he prefers Galadriel to Arwen. Arwen is never referred to as "the Morningstar". You may be confused by the dialogue between Gimli and Éomer:
‘But first I will plead this excuse,’ said Éomer. ‘Had I seen [Galadriel] in other company, I would have said all that you could wish. But now I will put Queen Arwen Evenstar first, and I am ready to do battle on my own part with any who deny me. Shall I call for my sword?’
Then Gimli bowed low. ‘Nay, you are excused for my part, lord,’ he said. ‘You have chosen the Evening; but my love is given to the Morning. And my heart forebodes that soon it will pass away for ever.’
The Lord of the Rings: The Return of the King, Many Partings, p. 305
Arwen's epessë ("after-name") is Undómiel, meaning "twilight star". It was translated into English as "Even[ing]star". There is no real explanation as to why Arwen was named "Evenstar", but my understanding (which may be wrong) is that it has two purposes:
- It recalls Lúthien's own epessë: Tinúviel, "Daughter of Twilight" or "Nightingale". Note that Lúthien is Arwen's great-great-great-grandmother and it was said that in Arwen, "the likeness of Lúthien had come on earth again."
- It shows nostalgia for the ages past, before Elves and their works started fading.
As for Gimli's answer above, it is a play on Arwen's epessë and the relative age between Arwen and Galadriel. At the time of the War of the Ring, Arwen is roughly 2,700 years old, but Galadriel is much older. Her age is not clear because she was born in Valinor before the Years of the Sun, but she could very well be over 10,000 years old.
Being born at the beginning of the Third Age, Arwen would represent the Elves' "evening", at the end of a long and tiresome day, while Galadriel would represent the Elves' "morning", when "the light of Aman was not yet dimmed in their eyes, and they were strong and swift, and deadly in anger, and their swords were long and terrible." Galadriel's golden hair also invokes images of a golden sun in the morning, compared to Arwen's dark hair.