This little square nut is what the seat bolts attach too to secure the seat to the floor. I'm needing new ones, but I don't know what the correct name is for this part, and I've been having a rough time finding it. Any help would be much appreciated. Thanks.

 

You will not find any like that as that type is crimped to the panel it is on.
You might be able to find a caged nut in the size you need, don't know if the right size it is just a picture I found of one.
http://www.steinertractor.com/IHS946...iABEgKf8PD_BwE

If it was me I would find grade 8 bolts & nuts with some large fender washers to spread the load out and nock washers to replace that nut you are holding.

Or you could tack weld that nut or new ones to the floor but again the load in at just that small point, a large fender washer spreads the load out over a larger area.
Dave ----

 

Thanks. I like your idea better.