Diode package designator?
There's not enough information given. D3515 (assuming it's not the reference designator) is probably something unique to your company, a pointer to a particular footprint or other database entry. 

If I look up 1N4148 on a distributor such as Digikey (which will find 1N4148xxxxx part numbers), I will find about a dozen different packages that are available from die to DO-213AA (the oh-so familiar through-hole glass package) to 0402 (0.04" x 0.02" surface mount), die etc. I might guess that it's the glass through-hole package but in 2019 it is probably more likely it's an SMT version of some kind. 

If the information does not exist in the EDA software, you can look up previous purchase orders for that part, physically go look at what is marked on the packaging, as someone who knows, etc. However, the information may (should) exist in the PCB design software. 

That will give you one manufacturer and one part number, which may help you find the distributor part number (though the distributor part number can vary with things like whether it's a reel or cut tape or bulk for the same product). If you look up what was ordered last time it should give you a hint. The PCB design software may list alternative manufacturers, not just one. 

So ideally, EDA software and/or physical evidence-> Manufacturer name(s) + Manufacturer part number(s) -> Distributor website (to look up their part number)

Chances are you'll have to interact with the designer(s) and purchasing folks during this process, otherwise you're probably not doing it right.