Clearly you weren't born here, as we (natives) never call it "the 101" or "the 237". That's a SoCal thing.
Yep, I am a SoCal transplant... it will be my 4th year here in the Bay Area this October. It is strange to my ears to refer to a freeway without "the".
I can tell Bay Area people natives by the lack of the use of "the" when referring to freeways (but that seems to be fading), the use of "hella/hecka" (which no SoCal native ever says) and asking what the concrete thing that divides a freeway is called (SoCal: Center Divider, Bay Area: Center Divide).
What confused me for a long time when I first got here is the traffic news and old road signs refers to the local name for the freeways like "The James Lick freeway is congested" or the "Bayshore Freeway, next right" (both referring to the 101). More confusingly, sometimes the signs will just say the next major city ("San Jose, next right" or "San Francisco, next left") without giving any hint that the sign is referring to a freeway or which specific freeway the sign is for. Newer signs now just have the Interstate/US Route symbol and freeway route number which makes things much easier.
It took me awhile to map the names to the numbers (which is how I keep track of things in my mind). That is also not to mention that the names are only for sections of the freeways and are only used and posted on a small sign where the section name starts.