If you don't want to claim your child as a dependent, you simply don't add her information in the Personal Info section of the return, so her name is not on your return.
Keep in mind that if she was under 24 at the end of 2018, and you met the qualifications to claim her but chose not to, she would not be able to claim the refundable part of the American Opportunity Credit. The IRS instructions for Form 8863 say:
If you were under age 24 at the end of 2018 and the conditions listed below apply to you, you cannot claim any part of the American opportunity credit as a refundable credit on your tax return. Instead, you can claim your allowed credit, figured in Part II, only as a nonrefundable credit to reduce your tax.
You don't qualify for a refundable American opportunity credit if 1 (a, b, or c), 2, and 3 below apply to you.
1.You were:
a.Under age 18 at the end of 2018, or
b.Age 18 at the end of 2018 and your earned income was less than one-half of your support or
c.Over age 18 and under age 24 at the end of 2018 and a full-time student and your earned income was less than one-half of your support (defined later).
2.At least one of your parents was alive at the end of 2018.
3.You're not filing a joint return for 2018.
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