You are almost close. Would you please try the following:
sed 's/^>.*PORGI_BACT/&_ORALMICROBIOME/' file.fa > outfile.fa
[Edit]
According to the OP's requirement, how about:
sed -E 's/^>.*(PORGI_BACT|HUMAN_MAM|TESTA_BACT)/&_ORALMICROBIOME/' file.fa > outfile.fa
Sample input as file.fa
:
>SEQ0|tr|Q7MX99|Q7MX99_PORGI_BACT
FQTWEEFSRAAEKLYLADPMKVRVVLKYRHVDGNLCIKVTDDLVCLVYRTDQAQDVKKIEKF
>SEQ1|tr|Q7MX88|Q7MX88_HUMAN_MAM
KYRTWEEFTRAAEKLYQADPMKVRVVLKYRHCDGNLCIKVTDDVVCLLYRTDQAQDVKKIEKFHSQLMRLME
LKVTDNKECLKFKTDQAQEAKKMEKLNNIFFTLM
>SEQ2|tr|Q7MX77|Q7MX77_TESTA_BACT
EEYQTWEEFARAAEKLYLTDPMKVRVVLKYRHCDGNLCMKVTDDAVCLQYKTDQAQDVKKVEKLHGK
>SEQ3|tr|Q7MX66|Q7MX66_DUMMY
MYQVWEEFSRAVEKLYLTDPMKVRVVLKYRHCDGNLCIKVTDNSVCLQYKTDQAQDVK
Output:
>SEQ0|tr|Q7MX99|Q7MX99_PORGI_BACT_ORALMICROBIOME
FQTWEEFSRAAEKLYLADPMKVRVVLKYRHVDGNLCIKVTDDLVCLVYRTDQAQDVKKIEKF
>SEQ1|tr|Q7MX88|Q7MX88_HUMAN_MAM_ORALMICROBIOME
KYRTWEEFTRAAEKLYQADPMKVRVVLKYRHCDGNLCIKVTDDVVCLLYRTDQAQDVKKIEKFHSQLMRLME
LKVTDNKECLKFKTDQAQEAKKMEKLNNIFFTLM
>SEQ2|tr|Q7MX77|Q7MX77_TESTA_BACT_ORALMICROBIOME
EEYQTWEEFARAAEKLYLTDPMKVRVVLKYRHCDGNLCMKVTDDAVCLQYKTDQAQDVKKVEKLHGK
>SEQ3|tr|Q7MX66|Q7MX66_DUMMY
MYQVWEEFSRAVEKLYLTDPMKVRVVLKYRHCDGNLCIKVTDNSVCLQYKTDQAQDVK
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