need a script to rename and resort TIF files

I have a group of TIF files with serial such as:

Im_000000

Im_000001

Im_000002

Im_000003

Im_000004

and I need to rename and resort them to be as follow

Im_000000.B

Im_000001.A

Im_000001.B

Im_000002.A

Im_000002.B

i use the below script, but it can only to rename the file with A and B without sorting

clear all; clc;

INDIV = 'C:\Users\Desktop\New folder\';
filenames_INDIV = dir(fullfile(INDIV, '*.tif'));
for filenum= 1 : numel(filenames_INDIV);
    if rem(filenum,2) == 0 
        [~, basename] = fileparts(filenames_INDIV(filenum).name);
        newname = sprintf('%s_%04d-imgA.tif', basename, filenum(:));
        
        movefile(fullfile(INDIV, filenames_INDIV(filenum).name), fullfile(INDIV, newname));
    end 
    if rem(filenum,2) == 1
        [~, basename] = fileparts(filenames_INDIV(filenum).name);
        newname = sprintf('%s_%04d-imgB.tif', basename, filenum(end,:));
        movefile(fullfile(INDIV, filenames_INDIV(filenum).name), fullfile(INDIV, newname));
    end
end

Answer 1

[Jan]

Folder = 'C:\Users\Desktop\New folder\';
Files  = dir(fullfile(Folder, '*.tif'));
Keys   = {'A', 'B'};

[~, name] = fileparts(Files{1});
name      = name(1:find(name == '_', 1, 'last'));  % Correct assumption?

for iFile = 1:numel(Files)
    newname = sprintf('%s_%06d%s.tif', ...
        name, ...                    % 'Im_07291355_'
        ceil((iFile - 1) / 2), ...   % '000000', '000001', '000001', ...
        Keys{rem(iFile, 2) + 1} );   % 'B' or 'A'
    disp(newname)  % Try it at forst before uncommenting:
    % movefile(fullfile(Folder, Files(iFile).name), fullfile(Folder, newname));
end

[Mohamed]

I tried the script, but this error apears to me:

>> [~, name] = fileparts(Files{1});

Brace indexing is not supported for variables of this type.

[Mohamed]

Many thanks, it works!!