Supposing your header range is A-K,
You could you use this formula from L2 onwards:
=IF(MID(TRIM(IF(A2=1,A$1,"")&IF(B2=1,", "&B$1,"")&IF(C2=1,", "&C$1,"")&IF(D2=1,", "&D$1,"")&IF(E2=1,", "&E$1,"")&IF(F2=1,", "&F$1,"")&IF(G2=1,", "&G$1,"")&IF(H2=1,", "&H$1,"")&IF(I2=1,", "&I$1,"")&IF(J2=1,", "&J$1,"")&IF(K2=1,", "&K$1,"")),1,2)=", ",MID(TRIM(IF(A2=1,A$1,"")&IF(B2=1,", "&B$1,"")&IF(C2=1,", "&$C$1,"")&IF(D2=1,", "&D$1,"")&IF(E2=1,", "&E$1,"")&IF(F2=1,", "&F$1,"")&IF(G2=1,", "&G$1,"")&IF(H2=1,", "&H$1,"")&IF(I2=1,", "&I$1,"")&IF(J2=1,", "&J$1,"")&IF(K2=1,", "&K$1,"")),3,1000),TRIM(IF(A2=1,A$1,"")&IF(B2=1,", "&B$1,"")&IF(C2=1,", "&C$1,"")&IF(D2=1,", "&D$1,"")&IF(E2=1,", "&E$1,"")&IF(F2=1,", "&F$1,"")&IF(G2=1,", "&G$1,"")&IF(H2=1,", "&H$1,"")&IF(I2=1,", "&I$1,"")&IF(J2=1,", "&J$1,"")&IF(K2=1,", "&K$1,"")))
This formula has a limit of 1000 character in column by the mid function. and it repeats 3 times the same formula because of the separator: ", " but if you dont mind the result format you can short it to one. just fill put 1 in columns and the column name will appear.
Hope this helps.