I figured the one who claimed him might be Evi The main reason being that he was succed into the Beyond instead of just out of Big T's clutches to somewhere else in the Cosmere.
I hadn't considered the possibility of Nohadon and I absolutely love this idea. In-universe amazing-king-guy who apparently has some sort of affinity with the Spiritual Realm, and we don't know whether he died? That's juicy rust. I'm imagining him still in there, just baking bread, chillin, and was able to wave airport marshalling wands and blow his whistle real loud to make sure Dalinar's passage through the Spiritual Realm to the Beyond was uninterrupted by Big T.
Dalinar's death was one of the very few we've seen so far where the character has accepted their death. He had a plan that he executed in his last waking moments as a hail mary for the Cosmere, saved Gav, he sent his goodbyes, and his dead body was discovered. The gag of the season story will be The Blackthorn being seen again, and it causing a trauma response for whoever, but then they learn it's Evil Dalinar so it's okay to kill him, even though he's leading Retri's armies, likely very effectively.
A Shard (or two) might be able to fight over a soul, but I feel like we'd see it going in a direction that isn't passing on. Dalinar didn't really have any Connection I could think of to any other Shard (aside from Culti, who if anything I could see ushering him Beyond like I said Nohadon could, but not claiming him for her own) so I think it's unlikely that Endowment, Valor, or another Shard did it. That being said, right when Big T takes up the power, it says
which is before Dalinar actually dies, so they very well may have been watching when Dalinar passed to the Beyond, even through time-dilation.
Honour's power was part of what said to Big T "You cannot have him," so I think we can definitely rule that or the Splinters out.
So basically I think it's either Nohadon or Evi, who is part of the Beyond, but this is weird and awkward because of, ya know, Navani.