How can I save an illustrator file with a white logo on a transparent background so the logo is visable in pdf so people I send the logo to don't think the pdf is blank. Others need to use the logo in different documents layered over different backgrounds.
There are a couple of different ways to handle this issue...
The first, simplest and my favoured approach is to have two separate files; one for use by people who are using the logo to build designs and artworks and one for people who just need to view the logo. The first file would have the logo set to white with a transparent background and the other would have a black (or some other colour) background added and would be marked as 'for viewing only' or similar. The only downside is that you sometimes need to send both files to people and rely on them to forward both on, but on the other hand you can choose to send just the appropriate file for the recipients needs.
The other option is to set up the white colour as a spot colour, called white (or 'white ink', 'prints white' or something like that) which is not actually white. There are various industry 'standards' for this (i.e. not really standard at all) which include using a pale pink or green colour (like 20% Magenta or 20% Yellow/Cyan). This means that the logo is visible to everyone, but when it is included in print jobs, the spot white colour is omitted (unless of course there is in fact white ink in the job), leaving a hole, which is generally that you want. The downside with this approach is that is looks 'wrong' to some people and can cause confusion. Also, it's pretty useless for digital.
I have seen one other approach, which is to put in a background (like in my first suggested option) which allows the white logo to be viewable, but place this on a separate layer (below the logo) which can be switched off in the PDF. This looks 'right' in a PDF viewer or email, but can also be used for creating artwork. As an artworker, I find this approach a little unfriendly, because I don't get a file that I can just drop in place without having to set the layer visibility to what it needs to be, but it's an option.
Your .pdf problem is, I think, no problem at all.. As long as you save your file as Pdf 1.4 or higher, you should be good to go. Pdf 1.4 is the earliest pdf version to support transparency.
I dont quite understand What you are are actually want in this question still
Since you said that " people I send the logo to don't think the pdf is blank", I'm assuming that you tried viewing the .pdf in acrobat ( or any other preview thingie you might have used ), which showed you a white background. I'd say that pretty much every .pdf capable viewing application has a default setting that shows a white background for convenience.
You can just try opening the .pdf in some editing application like Illustrator or Indesign or Photoshop to make sure, or In Acrobat settings Cmd+K > Page display > Transparency grid, you can turn on the view that shows you the transparency grid that is much like the one Photoshop has.
Hope this Helps