There are companies and individuals whose job is to take care of other persons' affairs for the other persons. If you do not have anyone to help you, you can looking into hiring professionals to handle your affairs for you. However, the fees charged by professionals are often rather expensive. Unless you have a sizeable amount of properties, the professionals may decline to accept you as a client.
The courts of your state may have registries of names of professionals who have met the courts' requirements to handle other persons' affairs.
Larger banks likely have departments that handle trusts and estates.
You can always start with attorneys.
I'm a big fan of family members over third parties being your executor or agent as they typically will do be there for you. However, if you have no one, then sure you can use a third party such as a cpa, financial advisor, lawyer, but remember they all charge fees for their services. If you do have someone you are thinking about but are on the fence, why not either use co-agent/co-trustees or implement a trust protector in a trust (ie, one who watches over the trustee). You should definitely go speak to a qualified attorney as there may be options or alternatives you might not have thought about. A good attorney will not only give you a straight answer, but also give you alternatives and help you think outside of the box. Hope this helps.
These are really two different types of jobs you are asking to help to fill, and I would add a 3rd -- a health care proxy (see # 2 below). Let me outline my thoughts on how to choose for each, in an admittedly morbid type of chronological order, for which I apologize to you in advance:
1) Power of Attorney -- is someone you have implicit trust to turn over all of your financial affairs. I realize that this not an easy step to take, but it is something we all need to have waiting in the wings. You claim that currently you have no one you can trust; I suggest that you really might if you think about it -- that there are people in this world who care about you and who are responsible people. If you really do not, then your first step is to try to cultivate such relationships with friends, family and an attorney you can trust.
2) Health Care Proxy -- this is the person that a doctor or hospital can consult with regarding your health care should one day, G-d forbid, there be a need to make a medical decision and you are incapable of making a decision at that time for whatever reason. Again, most likely a family member, but this person clearly needs to be your closest confident on life and death issues, not just the financial ones.
3) Executor -- this is the person who can carry out your wishes after you are gone in gathering your assets and distributing them as you set forth in your Will. This person could easily be the same person who chose as Power of Attorney, or it could be a family member, or even an attorney -- I would reiterate an earlier suggestion that you ask the person or persons you choose to be an executor not to take a separate executor's commission, especially if you choose a family member (there is language you can have your lawyer draft into your Will to accomplish this, and for the very expense, I do not recommend you name a bank or other institution to administer your Estate or be a Trustee under your Will (if there will be a need for one) for this reason).
With my summary and the previous answers, I believe you now have the components to make the right decision. But feel free to contact me if you have further questions. I wish you well.
Of course you can name someone un eithe rof those capacities, who is not related to you. If the problem is that you don't have ANY person close to you that you feel is trustworthy, then I would ask some questions of you about what it is that you find untrustworthy about all your relatives, and whether you really would have reason to trust a stanger more? Unless you are in a financial situation where money is no object and you can afford to establish a revocable living trust and name a paid professional trustee who works in a fiduiary capacity to manage your affairs for you, I woould suggest you work on developing a relationship of trust wiht some relative or friend. That will serve you well while you are still living and then you may wish to name the same individual as your executor in yoru will.