A = allData{1};
B = allData{2};
C = allData{3};

allNames = [A.names B.names C.names];

{A.names B.names C.names}

{A.names{1} A.names{2} ... A.names{end} B.names{1} ... B.names{end} ...}

allNames = cellfun(@(x) {char(x.names)},allData);
allNames = cellstr(char(allNames{:}));

>> allData{1} = struct('names',{{'hello'}},'junk',1:3);
>> allData{2} = struct('names',{{'hi' 'yo' 'hey' 'whassup'}});
>> allData{3} = struct('names',{{'howdy';'aloha'}},'junk',4);
>> allNames = cellfun(@(x) {char(x.names)},allData);
>> allNames = cellstr(char(allNames{:}))

allNames =

    'hello'
    'hi'
    'yo'
    'hey'
    'whassup'
    'howdy'
    'aloha'

allNames = cellfun(@(x) {reshape(x.names,[],1)},allData);
allNames = vertcat(allNames{:});

allNames = cellfun(@(x) {reshape(x.names,1,[])},allData);
allNames = [allNames{:}];

allNames = arrayfun(@(x) x.name, [allData{:}], 'UniformOutput', false)