Sevier County, Tennessee was a rural and sparsely populated county. Nevertheless, there were so many men named John Underwood in the county at the same time that a tax record once identified one of them as "John Underwood the red head". I have recorded this information in a note in RM, but I have not made "the red head" become part of the man's name.
On a more serious note, the problem you cite is a common one and can be a serious impediment to matching records with people and with identifying people properly in reports. I have even seen the Senior and Junior suffixes be used for men that I know were uncle and nephew or grandfather and grandson. I have even seen a case in a family bible where the Senior and Junior suffixes used for sisters with the same name (Elizabeth Bryan Sr. and Elizabeth Bryan Jr.), where the younger sister was named at her birth in memory of the older sister who had died.
I like the Elder and Younger terminology for your particular use case, but I doubt that one particular rule is ever going to cover every case that might ever arise. I think that some cases are likely to be so uncommon or so unusual or so difficult to figure out that only notes can adequately describe the situation. For example, there were two men Anderson County, Tennessee at the same time who were about the same age and who were both named John W. Peters. I'm about 99.9% sure that the two men were first cousins, and there were no Sr. and Jr. issues associated with them. But it can really be quite impossible in some cases ever to match a particular record with a specific one of the two men with any confidence.