I am not happy with the Agent of the financial company that manages my company's 403 b plan. Do I have an option as an employee to choose a different financial company and still have the company match my contribution?
Or I do not have a choice.

The employer has a lot of discretion to limit your choice of annuity providers. One possibility, though, would be to look into whether your preferred provider would agree to your transferring money from the company-provided annuity each month to an annuity issued by your preferred provider. Of course, if there are substantial withdrawal charges associated with the company-provided annuity, this may not be a practical option.
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Employee benefits legal resource site

Revenue ruling 90-24 permits the transfer of all or any portion of your account value to another 403(B) option of your choice. Realistically, you might want to consider transferring only portions which no longer have surrender charges - or even, the free withdrawal amount you are generally allowed under 403(B)(1) annuities.

Why don't you keep the TSA carrier and request a change of agent?

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