It might also be a
My name is not Jack, to many this is my name
It is not officially called jack, but it is often referred to as a headphone jack.
A mighty empire bought me to fame
It became very popular after it came out in Walkman, mighty empire being Sony.
Though now it is gone, I am still around
As we all know it iPhone 7 doesn't have a headphone jack anymore, but it is still widely used in basically every other phone and a bunch of other machines.
And sometimes I even make people feel proud
Some people might be proud of having it in their phone and mock those with iPhone 7.
Together I brought millions of people
People can connect with each other by speaking through headphones that connect to a headphone jack
Beneath me has died patriotic people
Was Steve Jobs patriotic?
A mish-mash of cultures, that's who I am
Regardless of culture, everyone uses a headphone jack.
Although the dragons do think, that I ignore them
Although dragons might think, headphone jack don't want none of that so he just ignores those dragons!
I know a few of the answers are quite far-fetched, but that's the only Jack I could think of while reading this riddle.