I personally would merge "JES" and "Jes Brieden" as @CatCat did in https://musicbrainz.org/edit/32178380. For me it looks like it's the same artist using 2 different artist credits.
As for "Beck" and "Beck Hansen" I wouldn't merge them, because the artist is also using other performance names such as "Mollüsk" and "Mr. Hansen". Funny enough, there's a "Thurston Moore / Beck Hansen / Tom Surgal" AC listed in "Beck" artist instead of being in "Beck Hansen".
As for "Andrew McMahon In The Wilderness", Discogs lists it as a separate entity, also the entity being a group, which is interesting. I haven't firmly decided yet, but if it's just a solo project and not a group, I'd be leaning towards merging it as well.
Are there any firm guidelines as to when should the artists be merged and when not to? I feel like the case is often that different people have different opinions about artist merges and the inconsistency is the result of those different people looking after their favorite artists, so in some cases they would be merged, in some cases they would be separate.