As far as I know,center-justification of uitable column names is not possible (as for r2021a).
A recent comment by MathWorks staff (Aug 2020) suggests a workaround that involves creating a second uitable placed above the main table, containing the header names and using uistyle to center the names. It wouldn't be too much work to put that together but it may require reworking existing code that assigns data to the UITable.
Update
An alternative would be to convert your table to a cell array and move the header names to the first row the array. A cell array is needed if your data are not all strings, otherwise you could use a string array.
Then you can format the table to make it look like it contains a true header row.
The table on the left is the standard UITable with a header-row (aka "ColumnNames").
The table on the right shows the results of moving the header row into the data array and formatting the table to appear as unchanged.
Note that this changes how the table will be indexed since data starts are row #2.
% T: your initial data stored in a table
T = array2table(rand(5,3),'VariableNames',["Lancaster","Cincinnati","Sofia"]);
% 1. Convert table to cell, move header names into row 1.
C = [T.Properties.VariableNames; table2cell(T)];
% Create two uitables for comparison
uifig = uifigure();
uifig.Position(3:4) = [ 679 420];
uitTable = uitable(uifig,'data',T,'Units','Normalize','Position',[.05 .05 .4 .8]);
uitCell = uitable(uifig,'data',C,'ColumnName',{},'RowName',{},'Units','Normalize','Position',[.55 .05 .4 .8]);
% Switch order of shaded rows
uitCell.BackgroundColor = flipud(uitCell.BackgroundColor);
% Center all cells of the table & bolden the first row
uisCenter = uistyle('HorizontalAlignment', 'center');
uisBold = uistyle('FontWeight','bold');
addStyle(uitTable, uisCenter)
addStyle(uitCell, uisCenter)
addStyle(uitCell, uisBold, 'row',1)
