Actually I am saving seeds and will offer up in seed swaps and wanted to be able to provide a variety rather than just a description, but if I can't get an ID I'll go the description route.

If bees that visited those plants also visited other pepper varieties first, your pepper seeds may result in a somewhat different fruit next year.

Since Peppers almost always self-pollinate, without assistance of bees, there is very little probability the seed will produce plants not true to the parent.

And, yes, I agree with theforgottenone that the fruit on the OP pic doesn't show the characteristics of the Round of Hungary peppers

Peppers are much more likely to cross than other "self pollinating" crops like tomatoes or beans. Before I starting bagging blooms when saving pepper seed I had them cross in my yard. And I have gotten pepper seeds in swaps that had been crossed pollinated, which is very frustrating when you expect one variety and wait months to find out it is something random. If one wants pure seed then one must take measures to prevent crossing. Granted, the likelihood of peppers crossing is totally dependent upon the amount of pollinators present in your location.

Rodney