Mass offerings should not be thought of as a payment to the priest for mentioning a name during Mass, but as a thanksgiving offering to God and His Church for the many blessings He has given us. A priest will not refuse a Mass intention only because there is no stipend attached (if he does, he has serious problems he needs to deal with). A parish worker who takes down the intentions may not be so understanding, but mistakenly so.
What happens with the stipends varies from diocese to diocese and sometimes from parish to parish. Sometimes it goes to the missions, sometimes it goes to the parish, sometimes it goes to the priest, sometimes it is divided up. A priest may only accept one stipend per day (to avoid abuse). Generally, in my diocese, the suggested offering is USD10, but we frequently get other amounts, from nothing to USD5 to USD30. The average is a little above USD10.
Most priests in the West are paid a salary. It ranges from barely above the poverty level to enough to be comfortable, but never enough to be wealthy. If a priest is wealthy, the money comes from family wealth or a previous occupation. Keep in mind that most priests have to pay from their salaries/stipends for such things as automobiles (and repairs thereof) and provide for their retirement and long-term care.
As for myself, I receive in stipends much less than I spend on unreimbursed expenses such as books and materials given to people I counsel or to our youth group and other items for which my parish has no budget. And I'm in a relatively wealthy parish in a very wealthy town.
Since I've been a priest, my bank account has not grown noticeably, and I've only been able to make a small provision for my retirement. That's even with an important contribution from family investments. I can't imagine how a priest who does not come from a well-to-do family, with student loans, in a poor parish, manages to get by without stipends.
To the poster that doubts if priests declare the mass offerings and stipends they receive in their tax declarations, I can't speak for anyone else, but I just did an hour ago.