No, sorry. We don't call people who assemble computers "Systems Integration Engineers", in English.
"Systems Integration Engineers" are designers and design level professionals, not assembly professionals, which is considered a "technician".
In addition, "Systems Integration Engineers" would generally be required to study engineering in the university, which would include math, science, and a host of engineering topics.
People who assemble computer are generally considered to be "blue collar workers" in the US, where "Systems Integration Engineers" are generally "white collar workers".
For example, if we go to a retail store and want someone to assemble a computer for us, we would likely ask "Do you have a computer technician here who can build a computer for me?" We would not expect this person to be a "white collar worker" with an engineering degree, nor would we expect to pay for that skill level. We would expect to pay the (lower) wages of a "blue collar worker".
The same is true if a large company was hiring people to assemble computers. They would generally advertise for a "Computer Technician" of perhaps a "Computer Assembler" (but I have rarely heard that term used).
It is not a matter of "hurting my ears", it is a matter of using the correct title based on education, training, expected salary, skill level, etc.
Generally, "Computer Technician" is the most accurate and widely used term. "Systems Integrator" is generally not used for someone who assembles computers; but it can be used if they build networks and integrate systems, not components of a computer system.
The original poster asked about the term used for people who build (assemble) computers, not integrate various computer systems and networks.
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OBTW, speaking of using a wiki as a reference:
Computer repair technician - Wikipedia, the free encyclopedia
Quote:
A computer repair technician is a person who repairs and maintains computers and servers. The technician's responsibilities may extend to include building or configuring new hardware, installing and updating software packages, and creating and maintaining computer networks. Computer repair technicians work in a variety of settings, encompassing both the public and private sectors. Because of the relative newness of the profession, institutions offer certificate and degree programs designed to prepare new technicians, but computer repairs are frequently performed by experienced and certified technicians who have little formal training in the field.[1]
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Also, one more reference:
Computer Technician
Quote:
A Computer Technician installs, modifies and makes minor repairs to microcomputer hardware and software systems, and provides technical assistance and training to system users. They also install or assist service personnel in installation of hardware and peripheral components, such as monitors, keyboards, printers and disk drives. They answer client inquiries in person and via telephone concerning systems operation; diagnose system hardware, software, and operator problems; and recommend or perform minor remedial actions to correct problems based on the knowledge of system operations.