I am not completely certain about the phrasing in your question: "add the file's name before each of the data sets". This is a potential way of getting filenames from the read of the datastore. Replace your existing call to readall with this loop. Every row of the table contains the name of the file in the first variable. The file name is repeated for all rows read from one file.
allData = ;
[data, info] = read(ssds);
data.Filename(:) = string(info.Filename);
allData = [allData; data];
data = allData;
data = movevars(data, "Filename", "Before", 1);