These names are from a list of 6000 names given to Finnish children (aged 1 to 10 years old). Some of the names may seem ordinary to Anglophones, but in Finland they're still considered rare and/or unique.
Lalli
LariLars-Antti
Lasu
LaszlóLaunoLauri-Mikael
Lauri-Olavi
Lauri-Pekka
Lauris
Lauri-Tapio
LeanderLeevi-Edvard
Leevi-Elmeri
Leimu - means "blaze" and "flare" in Finnish
Leino
Leis
Lemmy
Lenna
Lenne
Lenne Sámmol
Lenni /
LennyLenni-Eemil
Lenni-Jussi
Lenni-Lauri
Lenni-Luukas
Lenni-Matias
Lenni-Miikael
LennonLennu
LenoxLeon /
LéonLeonardLeonardoLeonel
LeonidLeo-Olavi
Leopekka
Leotrim
Lev
LeviLiamLias
Liinus /
LinusLiius
Lillebror - means "little brother" in Swedish
LincolnLionelLoisto - means "shine", "brilliance" and "splendor" in Finnish
LorenLorenzLorisLoui /
LouieLove / Lowe
Luc /
LukeLuca /
Luka / Luuka
Lucas /
Lukas /
LuukasLudvig /
LudwigLuisLyu