The version of Batman depicted in DC Universe's Titans does a poor job of maintaining his secret identity. Worse yet, this Dark Knight seems to have passed his lack of discretion on to both of his young squires, as both Robins show a similar inability to hide who they are and avoid attracting attention.
Batman's paranoia regarding his secret identity as billionaire playboy Bruce Wayne is well-known, even to those who don't regularly read comic books. For many years, Batman hid who he was from everyone on the Justice League apart from Superman, until dire circumstances required the entire team unmask themselves. The one glaring exception to this web of secrecy was when Dick Grayson formed a new Teen Titans and did little to try and hide the fact that the man who adopted him was also Batman.
Titans, season 2, episode 4, "Aqualad," reveals that the DC Universe series' version of Dick Grayson lacks a similar sense of caution when it comes to his mentor's secret identity. It is made clear that the rest of the Titans are aware who Batman is, as they make reference to him by using his first name, Bruce. The WayneTech logo can also be seen as a screen-saver on several of the monitors of the supercomputer (presumably modeled on the Bat Computer) in the basement of Titans' Tower. Granting that the tower is protected by biometric locks, this still seems like the sort of obvious clue that Batman would avoid leaving behind, branding be damned.
At the same time, it doesn't seem like this version of Batman has done much to train his young wards (who are both also attached to him in an official capacity in the public eye) in the arts of stealth and remaining unnoticed. The season 2 premiere saw Jason Todd, the second Robin, loudly shouting "Titans are back, bitches!" into a live television camera in broad daylight. Yet when it comes to failing to protect your secret identity, Dick Grayson is the king.
Titans season 1 opened with Dick trying to get away from his former life as Robin, while still using his real name to become a police detective in Detroit. He also showed a dangerous habit of going undercover without any attempt to disguise himself and questioning suspects unmasked. Ignoring that Dick is a good-looking man who tends to stick out in peoples's minds, one would presume he'd be at least moderately well-recognized as the adopted son of a noted industrialist and philanthropist like Bruce Wayne, even if he didn't have a horde of paparazzi following his every move. It seems then, as in the original comics, that Robin is more of a hindrance than a help when it comes to Batman maintaining a secret identity.