Nicholas - perhaps something liek the following could be used if the MyStructure is similar to yours.
MyStructure = ;
for k = 1:5
MyStructure(k).name = sprintf('filename_%d.txt', k);
strMatch = arrayfun(@(x)strcmp(x.name, 'filename_4.txt'), MyStructure)
We use arrayfun to a apply an anonymous function to each struct in your array. We compare the name of each to (in this case) the fourth file name. The strMatch variable is a logical array of ones and zeros. If there is a one, then that will tell you which index (and so row) the match is located in.