Here is a selection of some cool names for cats which all start with the letter H.
| Hagar | Hazel | Hocus |
| Hamilton | Hazelnut | Hogan |
| Hamlet | Hector | Holly |
| Hammy | Heidi | Hollywood |
| Hanibal | Hendrix | Homer |
| Hank | Henrietta | Honey |
| Hannah | Henry | Honeybee |
| Hans | Hera | Honeycat |
| Hansel | Herbie | Hope |
| Happy | Hercules | Horatio |
| Harlequin | Hermione | Hotshot |
| Harley | Hero | Houdini |
| Harold | Hershey | Howie |
| Harriet | Hickory | Hubert |
| Harrison | Hildegard | Huckleberry |
| Harry | Hissyfit | Huey |
| Harvey | Hitchcock | Hugo |
| Hattie | Hobbit | Humbug |
| Hawkeye | Hobgoblin | Humphrey |
| Hayden | Hobie | Hunny |
| Hayley | Hobo | Hunter |