I've never heard of the TUSA Tina. Only just looked at it based on this thread. Walmart does seem to sell a bunch of things that seem out of their wheelhouse. Usually, they aren't really sold by Walmart, but by other sellers/companies that list on Walmart.com. Seems to be the case here.
It will come down to personal preference. The Tina is a jacket style, while the Zena is a back inflate. I much prefer the back inflate style. For obvious reasons (I'm a guy) I don't dive with a Zena. I dive with a Stiletto. My oldest daughter has a Lazel (discontinued female version of the Stiletto), and my youngest daughter has a Zena. It's a solid BC and she likes it.
For the name thing, I saw things like these in my Facebook feed recently. So, you could still have your name on your BC.
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Zena is solid and there are lots of ways to expand.
The Zip mount adapters are pretty cool. Gives you options to mount a variety of different things to your sides just forward of the bladder.
One modification I made to all 3 BCs is to move the trim pockets. The trim pockets come on the lower strap, but I prefer them on the top strap as it's easier to trim that way. That did complicate mounting the Zip mount, but not too hard. I just had to install them upside down.