Either convert the single select into a formula field, or create a new formula field, with this formula:
DATETIME_FORMAT({Date Field}, "MMMM")
If you want to keep your original single select field, use an Automation to copy the value of the formula field into the single select whenever the value of the formula field changes. This is going to eat into your monthly allotment of automation runs so this may not be sustainable without using a script to reduce the number of times the automation should run.