It'd be perfectly reasonable if libpam-google-authenticator relied on Google's infrastructure, but despite the infelicitous name, it does not; it just implements the server side of TOTP. The authentication flow is identical to any other correct TOTP implementation, and you can use any compatible client; no integration with Google services or infrastructure is required. (In fact, I don't think it's even possible.)
Speaking of TOTP without Google, if you use iOS and find the Google Authenticator app unsatisfactory, try Authy. It's good stuff, and well worth a few bucks.
While I'm not in the market for an OTP client, this is the network tools app I've been looking for since I bought my first iPod Touch. If you have remote beer-buying support, point me to it.
I moved most of my 2FA/TOTP stuff to 1Password. Works great on the Apple watch, and it's one less app (I tried Authy, but I have this thing against using too many apps)
I've been thinking about starting to use a password manager (as I should've done long ago), and 1Password looks pretty good. It's pricey enough that I'd like to hear some pros and cons before I pull the trigger, though. How's it worked out for you? Where are the pain points?
FWIW, the desktop app has a free trial, and on top of that, the developer offers a 30-day money-back guarantee if you buy direct from their store. (Not sure about the mobile app, haven't used that.)
I use the desktop app every day and am generally happy with it. It has many thoughtful touches, like automatically clearing the clipboard a minute or so after you copy a password into it, so that you don't later paste your password into some other text field by accident.
Speaking of TOTP without Google, if you use iOS and find the Google Authenticator app unsatisfactory, try Authy. It's good stuff, and well worth a few bucks.