Can I have two versions of Huatli out at the same time even though they are the same planeswalker, just with different names?
Yes, you can have multiple Huatli planeswalkers on the battlefield at a time.
This is a recent change when it comes to magic, but planeswalkers are now Legendary permanents so planeswalker type is no longer considered for determining if it gets to stay on the field.
306.4.: Previously, planeswalkers were subject to a “planeswalker uniqueness rule” that stopped a player from controlling two planeswalkers of the same planeswalker type. This rule has been removed and planeswalker cards printed before this change have received errata in the Oracle card reference to have the legendary supertype. Like other legendary permanents, they are subject to the “legend rule” (see rule 704.5j).
704.5j: If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”
So as long as the two planeswalkers don't have the same card name, you can have them both on the battlefield simultaneously.
If those are the two cards you are meaning then no because of the Legendary Planeswalker - Huatli