Anyone familiar with this "occupation?"

[jdk1963]

This is the occupation as written in the lady's profile.

operator psychologist on telephone of the confidence

Would that be the suicide hotline?  Maybe the psychic friends network?

[SANDRO43]

That's an entirely new one . If you ever find out what it is supposed to mean, please let me know and I'll add a new entry to our Russglish Glossary (http://www.russianwomendiscussion.com/mwiki/index.php?title=Russglish_Glossary) .

[jdk1963]

Who would have ever thought to actually ask her?  I figured why not so I asked.  She wrote back and from what I can figure out it is something like a suicide help line. 

[Shadow]

In europe that are telephone numbers people can call if they need to talk to someone in confidence about their problems. It can be suicide, but also about abuse, problems with raising children and all such things.

[janic]

Would that be the suicide hotline? 

Yep, I would think so. - Without the psychologist I would rather tend to some FSB/SBU denunciation-hotline. But .... Well, all the three-letter-agencies employ lots of shrinks... Who knows.

Why don't you just ask her?

Greets, j.

[ukguy1977]

Whatever job it is I think she has probably used an online russian-english translator to get it into English for you, hence why it doesn't read well

[Tamara]

In europe that are telephone numbers people can call if they need to talk to someone in confidence about their problems. It can be suicide, but also about abuse, problems with raising children and all such things.

Another job title lost in translation.  But the question is easy to answer.  Like Shadow said there are services in Russia providing free telephone help to abused children and/or women, pregnant teenagers, people with STDs, alcoholics, etc.
The lady's job is to work in their call center in a position of an operator answering calls and providing psychological help to anonymous callers.