"Law & Order: Organized Crime" have went overboard with sending Elliot Stabler undercover

He was given quite an exposure at the press conference after the Brotherhood case (2nd season) and the coverage of its trial. Not to mention that even prior, Richard Wheatley literally made him go viral and forced him to introduce himself and share his biography to the world to prevent further harm than that Wheatley already caused, before Wheatley's own downfall (mid-Season 2).

It's like the writers don't care about their own created lore/universe.
The New-York City based criminals whom he infiltrated the most afterwards should have some suspicion about seeing his face somewhere before (I bet they have a TV/internet &/ read the newspapers where it was posted).

Having said that, the Organized Crime task force has Bobby Reyes who was introduced past the Brotherhood case in the third season; he prides himself for being able to blend into various situations due to being the typecast nobody pays attention to. Yet he gets underutilized for some weird reason and is quite a useless character most of the time.

I don't know what (besides Chris Meloni being the star of this show) led the writers put an (in-universe) Irish guy (with a high press/exposure profile) within a Dominican gang "for months" at the start of the 4th season of OC when Reyes (as proven in the 5th season) is the right man for such missions.