How do I run SUMIF formula only if certain criteria is met?

I want to sum a answer in a area, if I enter a name in cell L35, can it match the name from the picture of E21:I35, then sum the number under the name and show it in cell M35? But there are formula in cell E21:I35.

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Thank you so much, it works, but I do not understand why did you put "E23:I35,E22:I34"?

I think the answer to your question is that you are summing the cells below where the match is, hence the range is offset by a row