In other editions and games there is a skill called streetwise to use when -gathering rumours, -finding the likely location of the thieves guild,- tracking down someone who might be selling a desired item,- knowing the affiliation of some n'er do wells you bump into;or just finding a lost puppyI see from the PHB that it might be just a charisma check but that suggests that there is no learned element which seems wrong.What have you used?
I don't find the idea of boiling all this stuff down to a die roll to be a good one. As such, I don't find the idea of lumping all these barely related activities together in a single proficiency to be a good idea.
Instead, I would handle each situation you describe on a case-by-case basis, as follows:
Gathering Rumors: The player tells me where their character goes, and who they ask what questions, or at least who they attempt to overhear - and in almost all cases, I just give them info that makes sense for them to gain by doing whatever they did. Example: Player tells me their character heads to a local tavern, plops down a couple gold coins on the bar and says "A drink, barkeep, and the latest gossip if you've got it," and I tell the player the barkeep supplies a beverage, pockets the coins, and what gossip the barkeep shares.
Finding the likely location of the thieves guildThe player tells me how they are looking; a criminal background character might just get in touch with their contacts, are already know where it is; another sort of character might go about investigating and looking for clues (and might, but won't necessarily, end up rolling an Intelligence (Investigation) check in the process); and another still might simply bait a pickpocket with a display of wealth and then ask, or follow the thief to find the location. If the city is over-run enough with crime, it might even be so easy as to ask anyone where it is because everyone knows where the crime boss(es) hangs out and no one dares do anything against them.
Tracking down a seller of a desired itemSellers want to be found, so I never make this more difficult than the player saying "I ask around town to see if anyone is selling what I'm looking for."
Knowing the affiliation of some n'er do wells you bump intoIf they aren't wearing some indicator, don't give a name that you can have heard rumor about the affiliations of, aren't bragging about these affiliations or bringing them up for some other reason, or haven't been recently seen on a wanted poster that listed their affiliation - or the character has been told this information for certain in some other fashion - then you just don't know. Better ask somebody.
Finding a lost puppyThat's a tracking job, albeit a particular hard one, but is usually just a mix of asking people if they've seen the puppy, following any tracks that are found, or investigating any clues that are found should this "lost puppy" situation actually be a "puppy-napping". But the process is one that will require much more role-play and character input than "I roll X to find that puppy."
