I can't say I know the system in terms of horses, but in dogs, the first letter sound is less important than the long vowel sounds and the number of syllables. For example, rather than changing Dan to Digby, which is a completely different sound, you could change Dan to Zan or Van, or Chance, or Brant, something like that. However, if you are wanting to change to a completely different sound he WILL eventually learn his new name, it just sometimes takes a little longer. When I got my horses, I changed my gelding from "Ranger" to "Claymore", that was close enough he learned it promptly, but my mare went from "Dreamer" to "Freyja", which isn't close at all, however she didn't seem to particularly know her name or come when she was called, and it didn't take her much longer than Claymore to learn her new name. That was probably my fault though, I call her "Mama" as often as I call her by name - she responds to both now.
Personally, I'd change from Dan too, I'm not super fond of "people names" on horses, and since Dan is my ex's name I'm not loving it *lol* Your horse is lovely!