Thought-speech must still have different voices for different people
It's hard to find any solid evidence on this, but there seem to be enough clues to imply it. In book 1: The Invasion, Jake and Marco are able to identify Tobias in a brand new morph that they haven't previously seen and don't know he's acquired, before he identifies himself. This is also the first time Marco has heard Tobias use thought-speech, but he was still able to figure out who it is.
There was a bird there. Some kind of huge bird like an eagle or a hawk, beating its wings against the window.
<Let me in, all right? I can't hover here forever!>
Marco's eyes went wide. He'd heard it, too.
I opened the window and the bird flew straight in. It landed on my dresser. It was almost two feet long, mostly brown, with gnarled talons and a sharp, hooked beak.
"It's some kind of eagle or something," Marco said.
<A red-tailed hawk, actually,> Tobias said.
"Is that you, Tobias?" Marco demanded. "I thought we weren't going to do any more of this morphing."
This means, at the very least, it's possible to tell between male and female thought-speak voices, since Marco was able to guess accurately that it was Tobias rather than Rachel or Cassie (the questioning tone presumably more out of surprise than uncertainty).
However, we can answer this with a bit more certainty if we allow for a somewhat more questionable source: the Animorphs live-action TV series. In the show, thought-speech is represented essentially just with the character's normal voice with some reverb added onto it, thus everyone still has distinct voices which sound the same as talking out loud.
As for different voices for Andalites, assuming different people's thought-speak voices still "sounds" different and recognizable, it doesn't matter that Andalites can't speak out loud normally; their "voices" would still be able to sound distinct, and presumably do.