[ED. Da7e foolishly claims Iroh’s son was named Mako no Lu Ten. These instances have been corrected. Da7e will be flogged]
This is hard to pin-point because of the history of the name “Mako” as used on the series.
Uncle Iroh was voiced by Mako Iwamatsu, the actor, during Books 1 & 2 of Avatar: The Last Airbender. The “Tale of Iroh” is dedicated to Mako, – though Iroh’s son tragically killed son is named “Lu Ten”
However, it’s all complex now, because the Korra creative team has also mentioned that the Fire Ferret Mako was also named after the late voice actor.
Is Mako just a common Fire Nation name?
As for Mako being part of the Zuko bloodline, that might have roots in The Promise (Part One) and I discussed that a bit on Episode 1.
-Da7e-