You can't easily do that, but you can use a helper column that extracts a unique list from that range separately, then you name that new range and refer to it instead in your Data Validation.
So in a new cell, say B2, enter formula:
=IF(COUNTIF(A$2:A2,A2)=1,COUNT(B$1:B1)+1,"")
and copy down as far as you need
Then in a new column enter:
=IF(ROWS($A$1:$A1)>MAX(B:B),"",INDEX(A:A,MATCH(ROWS($A$1:$A1),B:B)))
and copy down as far as you want in order for new entries to populate...
Then change your Named Range, Month, formula to:
=OFFSET(Sheet1!$E$2,0,0,COUNTIF(Sheet1!$E:$E,"?*"),1)
where E2 is where you entered the extract formula above.
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