Feel free to use spelling variants and/or add more children :)
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Gabe Gabriel Gael Gage Galahad Galen Gallagher Gamaliel Gareth Garfield Garland Garrett Garrick Garth Garvan Gary Gaspar Gaston Gautier Gavin Gavril Gaylord Gebhard Gemariah Gemini Gene Gennadaius Geoffrey George Gerald Gerard Gerasimos Gereon Germain Gervais Gethin Ghislain Giacomo Giampaolo Giancarlo Gianluca Gianni Gil Gilbert Gilchrist Gilead Giles Gillespie Gioacchino Giovanni Giuliano Giuseppe Gladwin Glanville Glaucus Glenn Goban Godfrey Godric Gomer Gonzalo Goran Gordian Gordon Gore Gottlieb Govad Govannon Grady Graeme Grant Granville Gratian Gray Grayson Gregory Greir Gresham Griffin Griffith Grover Guillaume Gumarich Gunnar Gunther Gus Gustav Gwenael Gwilim Gwynn
GIRLS
Gabriella Gaia Gail Gala Gardenia Garnett Gavrilla Gay Gaynor Gemma Genesis Genette Geneva Genavieve Genista Georgette Georgia Geraldine Gerlinde Gertrude Gethsemane Ghislaine Giacinta Giada Gianna Gilah Gilbertine Gilda Gillian Ginger Giosetta Giselle Giulia Giuseppa Gladys Glenda Glenna Glenys Gloria Glory Godelieve Godiva Golda Goldie Gomer Gordana Grace Gracia Graciana Graciela Grainne Gratia Greer Greta Gretchen Greit Griselda Gry Guadalupe Guinivere Gulistan Gunda Gunhilda Gunvar Gussie Gusta Gwenda Gwenllian Gwendolyn Gwyneira Gwyneth Gypsy Gytha
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Hades Hadley Hadrian Hagan Hal Hale Hall Halstein Ham Hamilton Hamish Hamlet Hammond Hamon Hanan Hananiah Hank Hans Harding Harlan Harley Harold Harper Harris Harrison Hartley Harvey Haul Hayden Hazael Heath Heber Hector Heddwyn Heinrich Helder Helias Helios Helmfried Hemming Henderson Henrik Henry Herakles Herb Herbert Herman Hermes Hernando Hero Herod Heron Herschel Hevel Hewie Hieronymus Hilarion Hilary Hilbert Hildred Hiram Hob Hollis Homer Honorinus Hopkin Horace Horatio Horst Howard Howell Hrodger Hubert Hudson Hugh Hugo Hugues Humbert Humphrey Hunter Hyam Hyder
GIRLS
Hadassah Haf Hagne Haidee Halcyon Halina Halle Hannah Hannele Hannelore Happy Harmony Harriet Hathor Hava Haven Hayley Hazel Heather Heaven Hecate Hedwig Hefina Heidi Helah Helen Helena Helene Helga Heloise Hendrika Henna Hephzibah Hera Hermione Hersilia Hester Hesta Hilda Hildegard Hillary Hode Holly Honey Honor Honora Hope Hortense Hosanna Hristina Huguette Hyacinth Hypatia
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BOYS
Iagan Iago Ian Iben Iberto Ibrahim Icarus Ichabod Ichmael Idan Ignacio Igantius Iggy Igon Igor Ike Ilario Ilias Illarion Illiam Imelio Immanuel Imrich Increase Indiana Indigo Indio Inglebert Ingram Inigo Innes Innocent Ioakeim Ira Irvin Irving Irwin Isaac Isadore Isaiah Isaias Ishmael Israel Isom Italo Ives Ivory
GIRLS
Ianthe Iberia Icy Ida Idabelle Idamae Idella Idette Idril Ignacia Igraine Ilana Ilane Ilda Ilene Ilia Iliana Ilisa Ilithyia Illumination Iluminata Ilona Ilsa Imagine Imelda Immaculata Imogen Imperia Ina India Indiana Indigo Ines Infinity Ingeborg Inger Ingrid Inspire Iola Iolanthe Iona Iphigenia Ireland Irene Iris Irit Irmingard Isa Isabelle Iscah Isidora Isis Isla Isobel Isolde Italia Iva Ivanka Ivonne Ivy Ixchel