You know what it is; we don't need to go into it here. But there's more to it than you think.
So, let's just get this out of the way. When the time comes, she'll know. The resemblance will be unmistakable. However, it's possible to find out early using the Physician's HUD. Anyone with a Physician HUD can perform an analysis on an expectant mom to determine paternity, as well as other factors (e.g., viability, gender, etc.).
NOTE: this is how this used to work -- the paternity system was retired when the store moved in favor of just using the Physician HUD. If anyone would like to see this functionality come back, drop Eliot Hesse a note.
Historically, paternity testing was loosely modeled on Real Life. To participate, you needed to stop by the main store and drop off a blood sample with the "nurse." The clinic would keep the results on hand for a couple of months. Next, you needed to authorize the clinic to perform tests with your sample (i.e., let the nurse know who's authorized to perform a test). That's it. Your job was done. Your partner could come by whenever she liked and try to determine the father. If your sample was still on file and you gave consent, your partner would be notified that you're a papa. There was no difference in the results between not having provided a sample, and not having given consent -- the results would simply be inconclusive in both cases.
You might see something a little different from time to time when you couple with your partner. Your HUD will look like that image over on the right (sometimes the shape of the dark-red part is a little hard to discern, and might look more like a period). That just means things will be a little messy, and the chances of conception are just about nil. It's your choice as to whether to proceed, and you won't find out until you're well, underway. By the way, she knew, even if you didn't...
The male HUD allows you to find out how your partner has configured her HUD (e.g., what fertility options she's chosen). When coupled, you can click your HUD and choose the "Womb?" option to find out all of these settings. It's an opportunity to find out if your partner is gaming the system. It's her right to, but it's also your right to know. However, the HUD won't tell you anything else, such as whether she's already pregnant, where she is in her cycle, etc. Well, except for maybe that red dot over there...