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.
Ia / Iia
Iben
Ida-Alexandra
Ida-Emilia / Iida-Emilia
Ida-Ester
Ida-Kaisa
Ida-Lena
Ida-Liisa / Iida-Liisa
Ida-Lina
Ida-Louise
Ida-Loviisa
Ida-Maja / Iida-Maija
Ida-Olivia / Iida-Olivia
Idde
IdunIduna
Ieva-Maija
Ifraah
Iggie
Iida-Alina
Iida-Anniina
Iidaleena
Iida-Lotta
Iidamaria
Iidamarja
Iida-Marja
Iida-Milla
Iida-Sisko
Iisa /
Isa / Iza
Iisa-Alisa
Iisa-Olivia
Iisa-Riia
Iisa-Roosa
Iisa-Stiina
Iita
Iita-Amalia
Iita-Liisa
Iitamaria
Iita-Maria
Iitu
Iitu-Liinu
Iitumaria
IkramIlanaIlena
IlmaIlone
IltaImmaImmi
ImpiInaIna-Márjá
Inara
Inari
IndiaInes /
InezInessa
IngaInga-Briitta
Ingalill
Inga-Lotta
Inga-Maarit
Inga-Maria
Ingela
IngerIngridIngvil
Inkaliina
Inka-Liisa
Inka-Lilja
Inka-Maaret
Inka-Mari
Inka-Maria
Inka-Marja
Inka-Moona
Inka-Riina
Inker-Anni
InkeriInki
InnaInna-Elisabet
Inna-Lotta
Inna-Maria
Inni
Ino
Inu
IoannaIpeksu
IraIrenaIreneIrinaIrini
IrisIrjaIrka / Irkka
IrmaIrmeli / Irmelie
Isabel /
Isabelle / Izabel /
Izabelle
Isabella /
IzabellaIsabella-Grace
Isa-Erin
Isa-Li
Isa-Maria
Ise
Isela / Isella
Iselinn
IsisIslaIsla-Aurora
Islaja
Isla-Maria
Ismahaan
Isra