One of the outlaws that Beau Maverick met in his last episode ("Red Dog") was Kid Curran. The Kid rode into camp with his new bride, the 19 year old Erma. The Kid couldn't have been more than 21 himself; and as the episode played out, he wasn't going to get any older (thanks to his wife.)
As mentioned in an earlier post, I've placed this episode in 1874 or 1875. There was another show, my second favorite Western, called 'Alias Smith And Jones' and that took place in the mid-1880's. One of the two main characters was Kid Curry and was about 29 years old when the Trueniverse audience first met him. So in 1875, he was about the same age as Kid Curran.
If that all works out, then I don't think either one of them adopted the nickname of "Kid" because of the notoriety of the other. And because they both were older than the televersion of the real world outlaw named Kid Curry (Harvey Logan) - as well as the man whose name was adopted by Logan, George Curry - then I don't think either Kid Curry or Kid Curran were affected by FIS (Famous Impostor Syndrome*)
I don't know if the televersion of the real world Kid Curry gave a damn about the situation once his own reputation was being established. Since the other Kid Curry usually had his name linked to that of Hannibal Heyes, and was going by the alias of "Thaddeus Jones" anyway, the real Kid Curry must have figured it didn't make sense to seek retribution if there was any slight intended.
Besides he always had his hands full dealing with such problems as Bart Maverick impersonating Doc Holliday in Arizona (as seen in the 'High Chaparral' episode "The Doctor From Dodge". More on that later.....)
* Better known in the Wold Newton Universe as Famous Individual Syndrome or more specifically, Great Detective Syndrome.