Sorry for being late to the party on this one. Can you, without giving up too much personal info, give us an example of an app that still recognized your device after a factory reset?
Will you also describe the steps you take, or took, that brought you to this conclusion? Was it actually a factory reset or some other action?
For instance, I know you say that you do not have a Google account on the device, but how then are you getting apps? A linked Google account is needed to access apps from the Play Store. It used to be that a Google account was needed to activate an Android device without being limited to the very basic of uses.
Are you also saying that none of your apps require a log-in of any kind? If they do not have any log in what information are they providing that causes you to believe they remember you/your device?
Barring the need for a Google account to download and install apps, if only from the Play Store, I've had phones that pull up previously saved data after uninstalling and installing the same app again because uninstalls are not as complete as many make them seem. Often there are folders left on the device which could include some saved or archived data from a previous install. How strong or weak this is depends on the device and the OS version as newer, more recent versions of the OS, have many more securities built in.
What device do you have and what OS version are you using?
Let's not forget your SIM card, carrier account. Both of which are accessible when granting Phone permission to an app. This falls under reading the phone state, I believe. If not it is accessible in other ways through permissions.
These devices are mini data recorders and we literally feed them everything about our selves in ways we can't even count. In fact doing a factory reset with app recovery literally requires the device to record every app on the device so that it can reinstall them once the reset is complete. How can an app remember you, the question should be what are you doing to make the phone forget your apps.