The code below converts the numeric monthly observations into date format,
input month
1
2
3
4
5
6
7
8
9
10
11
12
end
clonevar monthname = month
format monthname %tmMonth
However, instead of 1 = January, Stata sees 1 = February, 2 = March etc.
month monthname
1 February
2 March
3 April
How can this be fixed?
With nothing else said, your syntax implies that your variable month (and any clone thereof) is a Stata monthly date variable, and thus follows the Stata rule that monthly dates are counted relative to an origin 0 in January 1960. Thus 1 is February [1960 also], and so on. Your particular display format suppresses display of the year, but it is still there as part of Stata's understanding -- given your format command.
Above all, assigning a particular display format does not convert a variable from one kind of date to another. See https://www.stata-journal.com/article.html?article=dm0067 for more on that.
If you want something else, you need some different syntax. For example, if your values are month of the year, and year is given otherwise, then you are likely to need to create monthly dates using a combination of month and year.