I know exactly what an UNO is, and you don't have one inside your product. At most your product is compatible with an UNO, but it doesn't have the R3 form factor afaics, so it's not that compatible.
My opinion is that you're using the Arduino name improperly, but that's a fight for the Arduino founders not me. Meantime I emailed them about your product and if they have issue with your use of the phrase "built-n Arduino UNO" or not, that's their call.
I'm out....