Oops, now I’m wrong. I decided to look at a 2005 CalTrans report instead of Google Maps. CalTrans says that the San Diego Freeway covers all of 405, then covers all of 5 from The Y to the intersection of 5 and 54 in San Diego. The portion of 5 from 54 to the Mexico Border is called the John J. Montgomery Freeway.
One slight difference, though, is in how the number is used. As the OP states, here in Southern California, the freeways are called “The”, then the number (such as “The 405,” “The 5,” etc.), whereas, in St. Louis, they’re referred to as highways, not freeways, and the designation is “Highway + the number,” such as “Highway 40,” “Highway 70,” etc. You would never hear a St. Louisan refer to “The 40”.
And as an implant to the SoCal area, I just have to say that I’m glad there’s far less of referring to the freeways by name than there seems to have been when I first moved out here, as it made it so hard to figure out where the hell you were or where you wanted to go, because most maps only showed the numbers, not the names. Not to mention that, IIRC, some of the freeways changed names, but not numbers, at various points along their route.
Which brings me to a bit of St. Louis Freeway trivia. . . Many moons ago, the highway now known only as 270 used to be numbered/named different on different stretches, based on which crossing highway you were headed towards, or “to.” So it went like this:
Between Highways 55 and 44, northbound lanes were 244 (“to” 44) and southbound lanes were 255 (“to” 55).
Between Highways 44 and 40, northbound lanes were 240, southbound lanes were 244.
Between Highways 40 and 70, northbound lanes were 270 and southbound lanes were 240.
As one might guess, this was extraordinarily confusing, and the 270 designation overrode all the others in the early '70s.
It’s not just SoCal that refers to a highway as “The #”. Years back, we saw an episode of the X Files where Mulder referred to meeting someone at a stop off “The 95”. It was set in/around Washington DC and “95” (or sometimes “I-95”) is the usual description for that highway. Not sure where Duchovny is from.
And a friend from Ontario recently referred to it as “The 95” when describing a driving trip to Florida.
Where do you think that episode was filmed, and where do you think the actors, screenwriters, director, producer, film crew etc. lived at the time, and how do you think the traffic reporter referred to the freeways they took to get to work that morning?
Doesn’t count. There’s an Ontario in the L.A. area too. 
Seriously, though, I think someone said recently in the Canadianisms-vs-Americanisms thread that Canadians generally use the “the #” format.
The latter also seemed to be the case in Northern California when I lived there. People would refer to the freeways and highways as “Highway 80”, “Highway 101”, or “Highway 1” without making a distinction on whether it was an Interstate, United States, or State route. Later, I noticed people started increasingly referring to interstates as, for example, “Interstate 5” or “I-5”. That’s pretty much the case here in the Pacific Northwest too. One sure way to know if somebody’s a visitor or has recently moved from Southern California is if they use definite articles when referring to our highways.
I wonder if somebody has ever thought of mapping the way people in various regions of the U.S. and Canada refer to highways and freeways (like, e.g., the “Pop vs. Soda” study).
Yes, this is the big Nor-Cal So-Cal debate/rivalry. At school I always get bugged with “Did you just say to take THE 80? You’re from So-Cal aren’t you?”. Its just a WORD people, get over it. And I will forever claim to be from Cen-Cal, so stuff it.