What do you call a profession who works with soldering iron? ?

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It is a basic skill not a real high profession'

I am pretty good at it ,, yet seldom is it in call for electronics in the field 

we do mostly board swap now days due to low cost boards verse field labor

swaptronics  -- isolate and replace 

I do not mean to be harsh,, but soldering on assembly line is not a high skill even if you are real good at it,,, many people are good at it,, 

the hard part is people on assembly lines leave after many years of good pay and find out they are not qualified for other work, and have to start pay scale all over again at the bottom 

assembly line work pays more/high because it is so boring that many people cannot stand it and leave  --- the pay is to keep you there to avoid constant training cost of new people 

sad part is most machines are Electromechanics and some chemical process.... learning the mechanics; and chemical application is the real hard part of repairs - not electronics .. being doing this since 1972 

the more it changes the more it stays the same 

The us of soldering irons is not restricted to any profession. I have a MSEE, and I sometimes use a soldering iron in my hobby. Probably the people who use them most are electronic technicians and general technicians who work  in a lab with engineers.

Some type of electronic assembly technician. 

PCB assembly technician. 

Not PCP.

In a modern plant these are done by machines not people. The machine which places components is called a pick and place machine. the one which does the soldering is called a wave solder machine. 

One profession which works with soldering irons is a TINKER (tin smith).                     

What you describe is an "assembler". Technicians and engineers also do this task, but not on a regular basis.

ELECTRONIC WORKER OR TECHNICIAN, BOTH  USE SOLDERING IRON DAILY IN THEIR WORKS.