Assuming that A1:L12 contains the data, let N2:N3 contain the unique names, such as Name1, Name2, Name3, then try the following formula which needs to be confirmed with CONTROL+SHIFT+ENTER, not just ENTER...
O2, copied dwn:
=SUM(IF($A$2:$A$12=N2,IF(MMULT(IF(ISNUMBER(MATCH($B$1:$L$1,{"Tr1","Tr8","Tr10"},0)),IF($B$2:$L$12=1,$B$2:$L$12,0),0),TRANSPOSE(COLUMN($B$2:$L$12)^0))=3,1)))
Alternatively, since it looks like the data within Columns B through L will contain 1's and 0's only, the following formula would suffice...
=SUM(IF($A$2:$A$12=N2,IF(MMULT(IF(ISNUMBER(MATCH($B$1:$L$1,{"Tr1","Tr8","Tr10"},0)),$B$2:$L$12,0),TRANSPOSE(COLUMN($B$2:$L$12)^0))=3,1)))
...which also needs to be confirmed with CONTROL+SHIFT+ENTER.
Hope this helps!