Extract month for column title

I'm working on a Gantt chart that extends out 90 days (horizontally) one day at a time from a minimum date in a vertical task range. This is typical of most project management spreadsheets.

What I want is to identify which month that date occurs.

example attached.

In the first column of the Gantt portion, I have a fixed date formated to display the date, that's easy. What I want, then, is automatically populate the cell above the first of the month with the name of that month.

I'm afraid that although the formula itself is straightforward enough, eg:

J2: =IF(OR(COLUMNS($J3:J3)=1,J$3=1),J$4,"")
copied across

the fundamental issue you have is

a) your use of merged cells (do not use)

b) width of column

An alternative would be to rotate the text orientation such that it appears at 90 degrees (ie vertical) & auto format row height.
I'd also be inclined to go with mmm-yy if using vertical setup.

Other than that you can't really do what you want given point b) specifically.