Any name sounded bad when someone said it like that. Hades just stood there. He kept his face expressionless, but internally he was horrified about what he'd just done. He should not have said anything at all, and instead he'd claimed the creature. The worst part was that this wasn't even the first time he'd thought about that name. He'd claimed a creature, and instead of making the goddess go away like he'd fully intended, Hades had somehow managed to walk all that distance with this goddess. They weren't walking anymore and she wasn't any closer to going away.
He'd shown her the dog. She'd got him to claim the dog. Now she wanted to find a place to bathe the dog. Why couldn't she attack or argue like a normal person? He was out of his element, and Hades wasn't quite sure how to respond. They were going in the opposite direction of parting ways. They were making plans, and it was hard to stop it all from happening, because Hades didn't want to interrupt her.
He was going to protest, but by that time she'd said being dirty was hurting the dog's skin. Hades was sure he was making a mess of being a ruler that day in ways that the others weren't, but if the dog's skin was being hurt like the goddess said, they needed to do something. It wasn't that he cared about the dog. But now he'd gone and named the thing. Naming the thing meant he had a duty to make sure its skin was fine. Hades knew they couldn't bathe it in her siblings rivers. He wasn't an idiot. The most hospitable looking one was the Lethe, and they'd just got back from him nearly drowning in it. But he didn't know the land well enough to know if there was any safe water.
“Are there any freshwater sources.. nearby?” Hades asked. He nearly said freshwater sources 'we could use' but avoided that at the last second. She probably wouldn't have thought anything of it. But the last time he'd been grouped like that, Hades had spent his life trapped, and in pain, and constricted in a dark place, and then a war. And they'd abandoned him immediately at the first chance to find sky. Hades did and didn't blame them. He'd find something else. He cast a sidelong look at the dog, and then whistled. The other four eyes opened.