No, you would not list them as your sons or you as their step mom. You would list them as "Another person" . The rules for claiming non relatives are different than for claiming a relative.
Did your boyfriend have any income? If he did, then you may not be able to claim his sons. Depending on who else lives in the household, you may not qualify as head of household for tax purposes. If you have children of your own, then you would be able to claim them to qualify as head of household and possibly for the child tax credits.
The best way to determine if you can claim them is to enter them on your return and click on the learn more links and answer each question carefully.
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