It would usually be the married name Phil, but if you can't find her under that name, I suppose you could check her maiden name too. People used whatever name they wished to, as many of us know. You could also try first name only if you can narrow down place and date of death or if she has an unusual first name.
Not all records have been transcribed as yet. There is information on the site which shows these statistics.
You can always ask for a lookup of the complete indexes on somewhere like Ancestry. Once again, if you can give details of dates and places this will help.