Yes it is possible. Aside from removing the user name from Excel, which in some versions requires a re-install of Office, here are two macros that you can assign to shortcut keys that will give you a default of no user name in new comments.
The first macro is bare-bones; it creates a new comment and keeps the comment box visible so you can click in it and edit it.
The second macro is heavier; it deletes the old comment if one was there, and sets the Visible property to False while putting you in edit mode to enter comment text, so it's more versatile. Some people hate invoking the SendKeys method, and that can indeed be a volatile proposition, but with some reasonable care you can use the SendKeys to your advantage, as in this case.
.Font.FontStyle = "Regular"
.Comment.Visible = True
On Error Resume Next
.Comment.Visible = False
If you want to remove the user name from pre-existing comments (macro author not known):
Dim cmt As Variant
Dim c As Variant
Set cmt = Worksheets("Sheet1").Comments
For Each c In cmt
c.Text "" & Right(c.Text, _
Len(c.Text) - InStr(c.Text, ":") - 1)
Caution: Only run the macro once in a worksheet. After the user name is removed, the comment is moved up to the first line of the comment box. Running the macro again will start deleting characters from the actual comment.