Anton is restricting access to this information
As the lead detective in charge of the investigation, Anton is deliberately making sure that no one makes this connection.
At one point junior detective Hugo asks Anton, 'What do we know about the eyelash, sir? Any family?' and Anton responds, 'I've already run the analysis - no living relatives.' [quotes approximate, from memory]. Anton is of course lying about Vincent not having relatives, so having 'already run' the analysis and explicitly shutting down Hugo's line of questioning implies that he is making sure others do not have access to this information. If he can control what the team working for him has access to, no one outside his team would have access to the names of suspects or the identities of samples.
Anton's control of the investigation is shown in a physical metaphor at the club, when another detective tries to collect the pill case on the table. Anton grabs his arm forcefully, preventing the detective from picking up the case, and then he takes it himself. These pills are Irene's heart medicine, but Anton actually thinks that it is Vincent's, since Vincent has a heart condition. Anton doesn't want to let anyone on the team collect any evidence about Vincent if he can help it.
In a later scene Anton is flipping back and forth between pictures of old Vincent and new Vincent-as-Jerome on a computer screen; he by now suspects that Vincent is using the identity of Jerome (but probably doesn't believe that he is physically impersonating him at work; perhaps it is just fraud or identity theft). Hugo walks in on him and says 'Isn't that the man from last night?' (when Vincent fled from them at the club) and Anton immediately shuts off the display and says 'He's no one'. It is clear that as much as he is trying to find Vincent, Anton is also making sure that no one else finds Vincent (or makes the connection to him), and he is deliberately blocking his team's access to crucial information.
Then, when Anton agrees to meet Vincent at Gattaca, he comes alone and tells Vincent that 'You're in a lot of trouble; I can get you out of here." Clearly he has not told his team about this meeting (they are all off celebrating the confession of the Director) and his goal is to remove Vincent from Gattaca without anyone on the police force understanding the connection between them.
Finally, in the deleted scene described by ssss, Hugo confronts Anton and explains that he has figured out the connection despite Anton's attempts to hide it.