"Come by after -Natalie" makes no sense
So Natalie and Jimmy used the backs of the little coasters as a communication method in their drug-dealing business.
This means that it was very common for them to read each other's notes, and were very familiar with each other's handwriting.
Why the heck would Natalie EVER need to SIGN the messages like that? As if Jimmy would be completely confused (think of Bill Burr's 'dumb guy voice'), and not be able to figure out WHO the heck wrote 'come by after'.
If ANYTHING, the address or at least the location would've been a good thing to add. 'Come by' without location is WAY more obscure and vague than the message would've been without her name on it.
Obviously Jimmy knows Natalie's schedule and where she'd be and all that, so that doesn't need to be written. But NEITHER does Natalie's name!
Furthermore, they are running a DRUG operation, and they just print their own names all over the place? What? Why would she risk anything, when she knows that:
1) Jimmy knows it's a note from Natalie, who else could it friggin' be?
2) Jimmy has been receiving multiple messages from her already in this fashion
When I think about it, does it even make any sense that she'd have to write ANYTHING? Isn't it already a routine, or otherwise a given that OF COURSE Jimmy would 'come by' 'after'? Would Jimmy just go to someone else's bar to talk with someone else, had Natalie not written that?
Of COURSE a boyfriend will come to the girlfriend's bar, just like he has done for who knows how long!
Then there's the whole - why would Natalie, a drug dealer's girlfriend - and we are talking about a drug dealer that can just have 200 grand in the back of a Jaguar, wearing expensive suit, etc., have to WORK, especially in a bar, unless it's just a cover for their drug business (which surely should be able to be done in a MUCH less laborious way, and the women would demand the MAN do the hard work anyway, if I have learned anything about this world)..
When you think about it, none of it makes sense whatsoever.