Have you tried:

MonthName(Month(Date) + 1)

For next month?

I haven't tested, on my phone but that's the first thing that popped into my head.

You can't add a date value to a text string. This is why you are getting a Type Mismatch Error.

Here is a sample. I used variable but you could easily modify the code to use form fields if you wish.
The important variable is d As Date used to add one month to the current date.

Dim currentMonthText As String, desiredMonth As String, reportMonth As String
Dim d As Date
    
currentMonthText = MonthName(Month(Date))
desiredMonth = "CURRENT"

If desiredMonth = "CURRENT" Then
    reportMonth = currentMonthText
ElseIf desiredMonth = "NEXT" Then
    d = DateAdd("m", 1, Date)
    reportMonth = MonthName(Month(d))
End If
    
MsgBox reportMonth

I think we need to know how desiredmonth is determined?

Kevin the If block will always be current? desiredmonth will never be next

Yeah. But I just set it up like that as an example. It's the wee hours of the morning here otherwise I would have built a full example with form fields and either a Combo Box or an Option Group to select Desired Month.

I know how that feels

DesiredMonth is a word, either CURRENT or NEXT and comes from an INPUT box by the user. "It is determined as What month report data do you want to see? This month data (CURRENT) or Next month data (NEXT)."  If CURRENT, I will determine the text value of the current month (MAY). If NEXT, I will determine the text value of the next month (June). RecordSoure will be based on a field containing the "text month". I determine this last data using DateAdd function:
( ReportMonth = DateAdd("m", 1, MonthName(Month(Date)))

You'll get a type mismatch using DateAdd("m", 1, MonthName(Month(Date))) because the DateAdd function is looking for the following types of parameters:

1st: String "m" defining you interval
2nd: Number, the number of intervals to add/subtract
3rd: Date (Variant), the date to add the number of intervals to

The problem is that you are trying to add 1 month to the date "May" which is not a valid date.

The solution I suggested above would be:

     ReportMonth = MonthName(Month(Date)+1)

Which would be:

     ReportMonth = MonthName(5 + 1)

or

     ReportMonth = "June"

Since Date is a number, Month(Date) would evaluate to a # between 1 and 12 (5, currently) and then 5 + 1 = 6 which MonthName(6) evaluates to "June"

If you want to keep the DateAdd Notation, you could also use:

     ReportMonth = MonthName(Month(DateAdd("m", 1, Date)))

Thank you all for your input.  Donald's answer (DateAdd) gave the perfect solution.  My hat is off to all y'all

Always happy to help