Hakun (Danish): Form of Haakon, derived from Old Norse name Hákon (high son). Its roots are há (high) and konr (descendant, son).
Haldan, Halden (Swedish): Form of modern Norwegian and Danish name Halfdan, which derives from Old Norse name Hálfdan. Its roots are hálfr (half) and Danr (Dane). Originally, it was used for half-Danish boys.
Hamdun (Moorish Arabic): “Praiseworthy, praise.” The feminine form is Hamduna.
Harik (Swedish): Form of Old Norse name Hárekr, from Ancient Germanic root ha (uncertain origin) and Old Norse ríkr (rich, distinguished, mighty).
Härjulf (Swedish): Form of Old Norse name Hæriulfr, ultimately descended from Proto–Norse name Hariwolfar. Its roots are hariar (warrior) and ulfr (wolf).
Härlek (Swedish): Form of Ancient Scandinavian name Herleikr, from roots herr (army) and leikr (fight, game, sport, play).
Härlög (Swedish): Form of Ancient Scandinavian name Herlaugr, derived from Old Norse name Hærlaugr. Its roots are herr and laug (to celebrate marriage, to swear a holy oath; to be dedicated, promised).
Hasten (Swedish, Danish): Form of Ancient Scandinavian and modern Icelandic name Hásteinn, from roots hár (high) and steinn (stone).
Haveron (English): Form of Harvey, derived from Breton name Haerviu (battle-worthy). Its roots are haer (battle) and viu (worthy). This name was borne by a 6th century Breton hermit who became patron saint of the blind.
Hemkil, Henkil (Swedish and Danish): Form of Ancient Scandinavian name Hæimkæll, from Old Norse roots heimr (home, house) and ketill (cauldron hat, helmet).
Heranal (Breton): I obviously wouldn’t recommend this name in the Anglophone world!
Heri (Scandinavian): Possibly a nickname for names starting in Herr, or from Old Norse word héri (hare, hare-hearted). This is still used in modern Faroese and Danish.
Hizquia (Judeo–Catalan): Form of Hezekiah (God strengthens).
Hopkin (English): Nickname for Robert. A lot of English nicknames which appear to make no linguistic sense arose from the custom of swapping letters. E.g., Rob became Hob, Rick became Dick, Meg became Peg, Will became Bill.
Humfroy (French): Form of Humphrey and Onfroi (peaceful warrior), from Ancient Germanic elements hun (bear cub, warrior) and frid (peace).
Halawa (Moorish Arabic): “Sweetness.”
Halhal (Moorish Arabic): “Agitation.”
Hamda (Moorish Arabic): Feminine form of Ahmed (more commendable).
Helissent (French): Possibly a form of Ancient Germanic name Alahsind, from roots alah (temple) and sinþs (path).
Helzbieta (Polish, Slavic): Form of Elizabeth, ultimately derived from Hebrew name Elisheva (“my God is abundance” or “my God is oath”).
Herannuen (Breton): From Old Breton root hoiarn (iron) and feminine suffix -uen.
Herborg (Swedish): From Old Norse roots harja or herr (army) and björg (help, protection). This name is used rarely in modern Swedish and Danish, though it’s somewhat more common in Norwegian, Icelandic, and Faroese.
Hereswith (English): From Ancient Germanic roots hari (army) and swinth (strong).
Herlinde (German): From Ancient Germanic roots hari and lind (linden tree, lime; soft, gentle; lime wood shield).
Hervor (Scandinavian): Form of Hervǫr, from Old Norse roots herr (army) and vár (woman; truth).
Hodierna (French): From Old French name Odierne, derived from Ancient Germanic name possibly made of elements od (wealth, riches, fortune) and gern (desiring, eager). The spelling was probably changed to resemble Latin word hodierna (present, of today, existing now).
Holuba (Polish, Slavic): “Pigeon, dove.”
Honesta (Italian): From a Latin word meaning “respected, reputable, distinguished, honourable.”
Hullah (Moorish Arabic): “Dress, garment.”
Human (Moorish Arabic): “Melted snow.”
Hunydd (Welsh): Possible from the Welsh word huan (sun) or hun (sleep).
Husa (German): Probably related to the modern German word Haus (house), as its dialect form is Hus.
Hyssop (English): A type of aromatic shrub from the mint family.