There are two methods here: Wait for them to ask you, or ask them yourself. Waiting is pretty self explanatory, just keep dating them and eventually after a successful date they may bring up becoming official. This can take a while tho!! Like, possibly weeks of ingame time.
And if you want to ask them: look at their schedule on their profile. Go to where they are in the evening and find them in the People tab. You should be able to approach them to talk, and you can propose a relationship from there.
Do note that depending on the NPC's inclinations and personality they might not want a relationship! They may very well say they're not ready or not looking for anything serious! It depends on the NPC.