Several points here. First, the people that you deal with don't have to accept a POA; they can insist on dealing directly with you.
Second, folks paying you money could send a check in your name care of your agent for your agent to handle for you once they have the POA. But they should not make the check out to your agent alone for several reasons.
- It raises issues for them in proving that they paid you what they owe you.
- They still will have to report any income you earned to the IRS as received by you--and making checks made solely out to your agent could raise difficulties in proving to the IRS what they paid you and may make it harder to prove their deductions.
Third, what you propose is dangerous for you. Having the account solely in the agent's name means the agent has sole control over your funds, with the possibility that you could lose those funds either to a creditor of the agent, or through negligence or outright theft by the agent. An account in your name with the agent as an authorized signatory doesn't eliminate all risk of troubles with the agent, but it does reduce it.
Fourth, understand that what you propose to do will not allow your funds to escape attachment by creditors. Those funds are still yours and attachable by your creditors once they meet the legal requirements to attach your assets.
What is the purpose of this arrangement? If it is merely for your convenience, then why not simply have the bank account opened with your name and with the agent as an authorized person? That would eliminate any problem with the bank accepting deposits made out to you, and would give you more control over the bank acocunt should you need it.