First of all, the entire premise is based on what Klinsmann famously did in 2003 - play for Orange County Blue Star under a pseudonym. Like so many things Klinsy, the story of why is a bit inconsistent - in one piece, Klinsy says the coach suggested the pseudonym (but why would the coach know or care to pick out Klinsy's home town as the last name?) - yet elsewhere, Klinsy has said he picked out his son's name, Jonathan, as his psuedo, but then wrote only the initial on the team sheet, leading everyone to call him Jay.
Of course, even if Klinsmann had written his real name, many wouldn't have recognized him anyway. LD is far more recognizable in the USA than Klinsmann ever was as a player. The idea that the Latino player on the rec squad here wouldn't recognize LD is pretty unfathomable.
Then there's the subtle dig at the very end of the commercial. LD has been left on the bench (like JK famously left LD off the 2014 World Cup roster) and it's very much played to the "what an idiot coach!" angle. That's unmistakably a JK slight, at least in my opinion.
Judge for yourself.