Is there a way to let customer see both the swatch and text label for it, like the “Option” setting suggests?
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I’m not sure I fully understand the question. What swatch are you referring to? Is this all with the settings on the Square Online Store? 
Yes, I would like to post pictures of this, but this forum website wont let me for some reason.
If you go to Items->Options in your Square Dashboard you can see options setup for Colors and Sizes of products that you have created. For colors you can choose to list it as just Text or as Text and Color. I have mine set to Text and Color.
Then when you look at the item in the Square Online store on the item page, you see that this change affected how the user can pick a t-shirt. I now see the color swatches. But there is no text next to the swatch, as the setting in Item->Options says that there should be.
Do you have the link to the item in the Square Online Store?