There is only one piece of information specifically regarding alignment change in D&D 5e
The Deck of Many Things (DMG, 162) Balance card says
Your mind suffers a wrenching alteration, causing your alignment to change.
This essentially swaps alignment. LE becomes CG, for example. In the Blood Hunter's case, CN would become LN. This card is intended for huge changes in play style that majorly affect the game. Switching from one end of the spectrum to another is a much larger change than switching from neutral to good.
Is it left intentionally up to the DM/players?
On PHB page 122, there is a small section on alignment that says
For many thinking creatures, alignment is a moral choice. Humans, dwarves, elves, and other humanoid races can choose whether to follow the paths of good or evil, law or chaos.
And explains that the good deities who created such races intentionally gave them free will.
An article of Unearthed Arcana from 2015 called Variant Rules also explains that
Alignment is meant to serve only as a quick summary of a character, not a rigid definitions. It's a starting point, but elements such as flaws and bonds paint a much more detailed picture of a character's identity.
From this we can conclude that alignment is not rigid and can be changed, but that this change should be the choice of the PC, not the DM since they have the free will to make that moral choice. That being said, as the DM, you could suggest an alignment change, or advise them that they are playing more CG than CN (once you know their intentions).
What are the affects of an alignment change?
There are very few mechanical effects of an alignment change, but here are all that I can find. I won't give a description of it, but I will provide the page number to see for yourself.
Robe of the Archmagi DMG, 194
Talisman of Pure Good/Ultimate Evil DMG, 207
In some cases, only characters of the same alignment of the artifact are able to attune with it. DMG, starting 214
When a character dies, they go to the plane of the deity they worship if applicable. If not, they go to the plane that corresponds with their alignment. So Arborea (CG) or Limbo (CN) for the Blood Hunter.