Depends. While we don't ordinarily capitalize such terms in general
writing, it's common practice for businesses to capitalize words like
"Company" (when the corporation refers to itself) or corporate titles
even when they are not attached to a name (President, News Director,
Customer Service Representative, so on.) "Customer Service,"
referring to a specific operation within the company might well be
capitalized in company letters and memos.
Also, resumes and similar documents are often stylized, capitalizing
the first letters of many terms that would ordinarily begin in lower
case.
But in general writing "customer service" would begin with a lower
case letter in most instances. Example: "I think that customer
service is a thing of the past."
You don't say, but I gather you may have been employed in the customer
service area at one time. If it's a job title or a specific operation
and your employer capitalized it, it is probably safe to do the same
when filling out applications--use your judgement. If the term is
general, as in my example above, you should not capitalize it.
BWB
It probably depends on where exactly in the resume you're writing the
words; I don't see that they need be capitalized in the body of the
resume, but it's almost inevitable that I'm going to be beaten over the
head with a style guide.