I was watching DS9 just now and it occurred to me: apparently in the future they have solved the problem of people having the same name. When talking via communicator you never hear "Sisko to Smith" and two different people try and respond. We've all worked in the place with two Bens or three Steves and there is confusion, but not in Starfleet.
The only logical conclusion is that the Federation assigns everyone a unique forename and surname at birth. Either that or you cannot be admitted to Starfleet if they have someone with your surname already.
Doc Freemo 
I would argue its better explained by ai being able to.infer who is meant even if more than one person has that name. Whichnisnpretty trivial to do well.
I dont tbink it would go like that st all. It woukd assume you mean whatever smith you interact with the most unless your working on something that would strongly imply a specific smith. If you want someone other than your closest colleague by that name youd include a first name.
@freemo @allstartrek I may have been joking. I'm pretty sure the cause is that the writers didn't want to have to deal with the issue. 
I suspect thw thought crossed their mind, it is prpbably even explained in one of the official technical manuals.
@freemo @allstartrek That's true! Maybe they'll do an episode on it like the one that explains why all the aliens are basically humans with things stuck to their faces.
Made perfect sense to me ;) lolol
Think of it another way if we the viewers can infer from a single name who thry are referimg to ao could an advanced ai that sees and hears all
@freemo @allstartrek
Computer: "Specify, Smith"
Captain: (Sighs) *Lieutenant* Smith
Computer: "Specify, Lieutenant Smith"
Captain: "Dammit, Lieutenant Steven Smith"
Computer: "There is no Lieutenant Dammit Smith on the crew manifest."
Can you imagine the first week at Starfleet Academy? Or a starship with a disproportionately Welsh crew so there are like ten each called Williams or Jones?