You likely just need to go into your Control's settings and give it a proper Control Name instead of just a label. 

1. What is "proper Control Name"?

2. What is "label"?

I imagine you mean the XML generated by the repeating section

It depends on the type of form.

If you use a Nintex New Responsive Form => this is normal, this is the current operation.

If you use Nintex classic form  and you have set a name of your control (name of the control in the Form designer) this should not happen.

Thank you, @nico 

Does Office 365's Responsive Form really behave differently from the On Prem on in this regard?

On Prim, all you need to do is to name the Control even in Responsive Forms for the XML to be correctly generated, just like Classic. 

Test Form with a Choice Control inside of a Repeating Section

Choice Control's Settings, showing the Control Name

Resulting XML from a test: 

is this different in 365? 

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@youmatsu wrote:

1. What is "proper Control Name"?

2. What is "label"?

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When you click on a Control that's on your form you'll see it's basic configuration open on the top ribbon, the "Control Name" I'm referring to is the "Name", and the "Label" is just called "Title" (which was my forgetfulness getting the better of me). 

(showing a control selected)

(showing the information on the top ribbon)

You can also double click on the Control and open the Settings of that Control, and you will find the same info: 

Setting that name should make the XML look a little more readable (assuming that Nintex roughly works the same in 365 land as it does On Premise):