The quotation marks are not actually part of the string. It is just displayed that way. Plus, since you are using strings instead of character vectors, you don't need to put them in a cell array. You can use a string array (with regular parentheses instead of curly braces):
folder_name_dia = linspace(0.05,5,100); % used to create an automatic string
for p = 1:length(folder_name_dia)
test(p) = "diam_" + folder_name_dia(p);
end
test = test';
test(1) % this shows the quotation marks to give you an indication that this is a string
disp(test(1)) % this just shows the string itself which doesn't actually have any quotation marks
