This is exactly what they did with 4G. For a while, if you saw that you had a 4G logo on your status bar, you knew you had 3G, but if you saw LTE, then you had real 4G. The only time you had 4G was when it didn't say 4G!
And I have to say "original definition", because the ITU eventually threw up its hands and said "fine, whatever y'all are calling 4G is 4G now!"
In technical circles, 4G was used as a synonym for the IMT-Advanced spec, but that was just common courtesy. And then post-HSPA technologies like HSPA+, Mobile WiMAX, and LTE showed up, and every carrier that implemented them called them 4G, and the ITU couldn't do anything. Eventually they published a nothingburger of a press release saying that they don't care anymore and as far as they're concerned, anything the carriers are calling 4G is 4G.
Of course, I had recently switched from ATT to Tmobile, so I'm not sure whether AT&T's HSPA+ was on paper speed equivalent to TMobile's LTE, but the difference in experience was amazing (it could also have been the fact that TMO had planned additional capacity before everyone joined - AT&T was crowded/oversubscribed for sure - or maybe the iPhone4S modem was just slower in general than the iPhone5).
AT&T was stuck on 21 Mbps vanilla HSPA+, while T-Mobile rolled out 42 Mbps DC-HSPA+ in 2011 (with a surprise midnight announcement that they'd already converted a huge chunk of their network and just turned it on). DC-HSPA+ had real-world performance better than or equal to AT&T and Verizon's LTE networks at the time, which were allegedly 100 Mbps but didn't perform like it, so I honestly don't blame T-Mobile for marketing it as being equal to Verizon's network. For context, this was back when AT&T was trying to buy T-Mobile, and the reason why T-Mobile was enthusiastic about it was because they were out of spectrum and didn't have any room to roll out LTE. So instead they went all-out in making their HSPA+ network as fantastic as possible until they could get bought by somebody with spectrum (i.e. AT&T). Rolling out DC-HSPA+ ahead of schedule was just the start; they had plans to follow that up with MIMO bringing speeds up to 84 Mbps. But then government interference caused the deal to fall through, which triggered a trap clause that forced AT&T to cede a decent chunk of spectrum to T-Mobile, so they scrapped their MIMO plans and rolled out LTE on their newly-acquired spectrum.
And they very much had an incentive to make their LTE network fantastic, because they needed it to perform better than their DC-HSPA+ network to be worth it for people to buy new phones. Being newer than AT&T's and Verizon's LTE networks (and maybe Sprint's, but I can't remember if Sprint switched to LTE before or after this) probably helped them, as they got to start it out with all-new hardware.
AT&T and T-Mobile both marketed HSPA+ as 4G. IIRC, T-Mobile did it first, and AT&T followed suit. It wasn't just a US thing either, because Canadian carriers also followed our lead and did the same thing.
Sprint marketed WiMax as 4G. They were the first to market anything as 4G in the US.
Verizon marketed the original version of LTE as 4G. While LTE-Advanced meets the IMT-Advanced spec, original LTE doesn't. And then as Sprint, AT&T, and T-Mobile all rolled out their LTE networks, they marketed them as "4G LTE" even though they too were using original LTE and not LTE-Advanced.
I had an EVO 4G