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.
Iakov
IanIbIbrahem /
IbrahimIdanIdriss
Ievgen
IggyIgorIidar
Iika /
IikkaIipo
Iippa
IiroIiro-Eevert
Iisac / Iisak / Isac /
IsakIisakkiIisko / Isko
Iisko-Henrik
Iisko-Jouni
Iisku
Iivari
Iivo
Iivo-Eerik
Iklas
Ikuma
IlariIlia / Ilja /
IlyaIlian
Ilias / Iliyas / Ilyaas
Ilkka
Ilmar
Ilmo
Ilo - means "joy" in Finnish
Ilpo
ImadImmo
Immu
ImranIndigo
IndyInko
Inno
IntoIoakim
IonIonafan
IosifIska
IsmailIsmoIsraelIssát
Isto
IvanIvar / Ivvár
Ivor