Ensign Eager was a nickname given to Harry Kim by The Doctor after the ensign suffered from an anxiety attack in 2376, something he had never experienced before.
The Doctor suggested it may have been due to the stress of having been on a two week away mission and immediately returning to normal duty upon his return to USS Voyager. The thus-christened "Ensign Eager" was diagnosed with exhaustion and given two days off. (VOY: "Memorial")
Tom Paris referred to him by this moniker in 2377 after seeing Kim's enthusiasm about returning to Voyager so Irina could find a spare part for her ship. (VOY: "Drive")