The sun produces 3.826 x 1026 joules of energy every second as it combines smaller hydrogen atoms into larger helium atoms. what is the name of the process which allows for the production of so much energy?

Well, the quantity alone doesn't point to any one particular process.
I mean, you could get 3.826 x 10²⁶ watts of heat out of a pile of
smoldering charcoal IF the pile was big enough and you kept it
supplied with enough oxygen.

The thing about the sun is that ==> it can churn out energy at that rate
from the mass that it has, ==> it has already been doing that for so many
billions of years, and ==> it will continue doing that for so many more
billions of years in the future.

The only possible process able to accomplish that is nuclear fusion.

So what is the question