Man No-Wan asked this oen a long long time ago and I just haven't been active in talk about stuff like this lately...
Basically, if you're going by games (which tend to be the only source info on squads and whatnot, there isn't a ton to go on otherwise), fighter squadrons have less a specific craft and more that pilots are trained on various craft and assigned what is suitable for the mission or a rotation system or whatnot...
Specific pilots assigned specific ships is not necessarilly a rarity, but it's maybe something done for base squadrons perhaps, or for the "elite"... But even then that's not necessarilly the "truth" as it were. For instance Rogue Squadron are known for being X-Wingers of course, but if you keep the games as part of the Rogue Squad story (which I do) then the RS'ers could fly A, B, X, Y, or even possibly other fighters into battle... I envision that they have full complements of vessels to pick from for their entire squad, and RS probably (logically) would also have what ammounted to a "minor league" team too... Kind of A team and B team versions of Rogue Squadron...
Let's say for arguments sake that Hoth is stationed (and Yavin) with JUST Rogue Squadron... They're just a planetary squadrion at Yavin, no "Rogue" yet, but they get that later on due to their exploits... Anyway, they have a plethora of fighters available to them, and they have way more than a dozen pilots as well, but there's like the "First String" 12 who make up the core... From there they rotate the "2nd string" in as needed due to casualties or fatigue... They'd act as any other squadron in the Alliance and this fits with the games pretty well for this squad.
One could argue that they change after Endor to kind of a "Special Forces" squadron that only use X-Wings or some such of course, but up till then and maybe some years afterwards, they're a regular squadron assigned to what maybe is the "core" alliance base... not the ONLY alliance base, but maybe their best and most effective scalpal agains the Empire. At least that's how I viewed it...
Anyway, this topic's about TIE Bombers and so I gotta get back on track with that...
The way games were set up, such as TIE Fighter had Bomber squads as basically just part of the rotation of any fighter-carrying vessel... Basically the ship is equipped with X # of Pilots, and they're the squad(s)... These pilots are trained on all fighter types within the Empire from hyper-capable like the Starwing Gunboat to the TIE series craft... During any engagement, you could be assigned to fly a TIE Fighter, or Bomber, whatever... In TIE Fighter, the names of squads deployed into battle were very blanket simple names of Alpha, Beta, Delta, Gamma, etc.... Usually Gunboat groups were listed Tau, Mu, Nu, etc... bombers seemed to generally be like Zeta, Eta, etc.
But they were the same pilots... It wasn't like there was a squad of pilots for Gunboats and things. This is partly for the game's dynamics of course, but when you think about it, Star Wars is a pretty (seemingly) static universe in that anyone can jump in any ship and fly... or at least fighters seem that way to an extent. So it's reasonable to assume that at least inter-group ships like Imperial vessels would be built similar and fly similar.
So anyway, if No-Wan is still reading and finds this, hopefully it's answers to an extent... The issues of insignia and things, I think it's pretty much a matter of either the Empire didn't allow it, or squads are just generic numeric designations like the "327th Fighter Squadron Assigned To the ISD2 Viscount" or some **** like that... Nothing flashy, though I could see them adopting a logo maybe for their mess hall but nothing they'd wear on uniforms or mark on ships.
Like maybe a polar bear (walk with me here) on a blue circle background is a patch they have for the "squadron" aboard some Destroyer somewhere, and they call themselves the "Ice" squadron, but to the Empire and in any formal ceremony they're the 327th and those logos are not seen or displayed anywhere but in the pilot's bunks and such... If that makes sense.
Plus of course, the pilots aren't "Bomber" Pilots, but rahter they're just Imperial Pilots who may be flying a bomber, a fighter, an interceptor or whatever depending on what their CO assigns them for any given mission.
Hope that makes sense...