How to get the month name in English using Numbers?
Without changing the localization language in your system, you could do something like this:

Create a table in a separate tab and Lock/hide it later
Then, in English add the month names in order from January to December in one column.  (A1-A12) [Be sure to set the cells as Text so that they don't show the localized names]
Change your formula to refer to the correct month name based on the month number.  Lots of nested IF()'s but if the MONTH(TODAY) is placed in a cell in the utility table, that will make the formula a bit more manageable.
Thanks to the OP for suggesting it in the comments!
place this formula in a cell then reference that cell in your original formula

Of course you can hard code the month names in the formulas, but then you would have to redo it in each instance if you changed languages.  This way you can just change the text in the reference table without breaking your formula.  Also, if you need the month name elsewhere, there is no need to re-enter the formula, just refer to the cell containing it.



EDIT
A simpler formula (takes getting used to, though) is to use INDEX(MATCH())
I actually use this method in a expense sheet I keep for English and French.

First I create a table with the numbers for each month and then text for each month in the target language.
Get the date
Use INDEX ( MonthTextLang, MATCH ( MonthNumber, NumberColumn ))

INDEX ( &quot;English&quot;, MATCH ( MONTH ( TODAY )), NumberColumn ))