On one character, my light cruiser is the USS Sito. Named for Ensign Sito by Picard, after the mission where she lost her life was declassified.
My other character's science vessel is a NX testbed platform named USS Mab, for the Faerie Queen of Air and Darkness. The ship is supposed to be testing a multitude of ECM/ECCM fleet support technologies, so I felt the name fit symbolically.
One of these, a Miranda-class light cruiser, I named U.S.S. Prospero.
I checked up on the Miranda-class on Memory Alpha, in search of inspiration and I would out that the class' name came from a character from the Shakespearan play, The Tempest. I search of a related name following those origins and in homage of Patrick Stewart, I decided to name my ship after Miranda's father Prospero, the protagonist of the play.
The other was a Shikahr-class light cruiser, the U.S.S. Kir-Shara.
I named the vessel after the vulcan artifact of the same name. This artifact that contained the writings of Surak and had a profound impact on Earth/Vulcan relations close to the very beginnings of the United Federation of Planets, when the founding worlds of the Federation started interacting more together (as shown in season 4 of the Enterprise series).
My Vesper-class cruiser I named U.S.S. Hesperus.
The name Vesper stands for 'evening', but it is also the name of a Roman god. "Hesperus" is how that Roman god was known to the greeks, so, I decided to pick the name. I actually liked "Vesper" very much and wanted to use it... but everytime I see a player with such a ship name (I pass by a Centaur and see it named U.S.S. Centaur) I tend to view that as unimaginative, with perhaps a little scorn at the 'cheap name... especially considering that as a player I could actually run into the NPC U.S.S. Vesper too. So, Hesperus was my compromise.
My Dakota-class cruiser I named U.S.S. Santee.
The Cheyenne and Dakota classes are named after native american tribes. I decided to follow suit and name my vessel after another Sioux tribe. Therefore, the Santee.
My Galaxy-class exploration cruiser I named U.S.S. Concordia.
Truth be told, I had no clue what to name my Galaxy-class. So, I just flipped through random names, found one that reminded me of the French Concorde plane, and tweaked the name slightly to Concordia.
U.S.S. Darwin - name of the "ship" I was given in a Star Trek video game group a long time ago - a group of people that liked to use Mac computers - so they named my ship after the architecture underlying mac OS X. I also believe in evolution, etc. so it's just a good name.
U.S.S. Itasca - Randomly assigned but when it did I couldn't believe it. I live in Minnesota and love my river, have been to Lake Itasca many times, and was amazed that a random name generator/assigner picked one that was perfect for me!