I would have used a text cursor, but, the recorded Macro is trivially modified to remove the font name, you just need to know that you can do that 
sub insertAlphaNoFont
rem ----------------------------------------------------------------------
rem define variables
dim document as object
dim dispatcher as object
rem ----------------------------------------------------------------------
rem get access to the document
document = ThisComponent.CurrentController.Frame
dispatcher = createUnoService("com.sun.star.frame.DispatchHelper")
rem ----------------------------------------------------------------------
dim args1(0) as new com.sun.star.beans.PropertyValue
args1(0).Name = "Symbols"
args1(0).Value = "α"
dispatcher.executeDispatch(document, ".uno:InsertSymbol", "", 0, args1())
end Sub
Lot easier than another solution (if you really did need the font name), which would look at the text cursor and pull the current font and use that. Inserting text at a text cursor (view cursor) should also not have needed a font.
if I wrote a macro that inserts the letter 'X', I would not expect the
insertion to specify the font unless I went out of my way to do so.
I am interested in seeing the macro that you are using.
Well, I am not actually "writing" the macro - I have no idea how to do
that.
I use "Tools -> Macros -> Record macro" and open the "insert special
characters dialog box".
THIS is where the problem is.
As far as I can tell, there is no way NOT to select a font in that dialog.
On top you have the "Search / Font / Subset" fields.
"Font" gives you a list of fonts, but not the choice of "none /
automatic" etc. - or allows you to delete the currently selected font.
I had been hoping to find that kind of choice.
Mr. Pitonyak. Please don't worry. I am not in a hurry. I have been
pondering this for years already ...
Thank you.
Thomas Blasejewicz