There are several tactics that I use at various times.
First, on WikiTree, the obvious one is to refer to them by their WikiTree # such as Katter–1234. Ditto on FamilySearch.
Another way is to refer to them by birthdate, e.g. Heinrich b. 1777 and Heinrich b. 1769. This can be useful if you know the birthdates and you're confident in the information. Less so if you end up trying to refer to Heinrich b. about 1770 and Heinrich b. about 1772. In that case a more detailed descriptor that's some combination of date-place-spouse is needed, such as Heinrich Katter of Randolph County who married Nancy Jones circa 1755.
You can also refer to them with a brief descriptor like "Big John Mayes" or "William May the Planter." The May Family DNA project uses both this method and the previously mentioned date-place-spouse differentiators.
Large family associations assign each person an ID number. Those numbers can be really useful when you're discussing ancestors with other descendants and trying to make distinctions or when reading research papers. Usually the association assigns a whole lineage a letter and then uses a numbering system in combination with the letter. These can be useful for family associations or one name studies, and using known IDs can be helpful to others. But I wouldn't bother making them up to deal with a handful of confusing people.
You can see examples of this on the Yoder Newsletter website or the Parke Society. For the Yoders, Hans Yoder of Great Swamp is YB, then his children are YB1, YB2, etc. Their children are YB11, YB12, YB21, YB22, etc. The Parkes IDs are generation number-lineage letter-family group #. Robert Parke is 01K1, his children are 02K1, 02K1, etc., the next generation is 03K1, 03K2 and so on. Both give every person a unique ID. The Yoder system makes it clear whose children are whose within the numbering system.
What I wouldn't do is number people using Roman numerals. In the U.S. and Western Europe those numbers suggest certain relationships and descent and are usually taken as part of someone's name. Not terrible if they're known grandfather-father-son, but confusing if they're an array of cousins, uncles, sons, grandfathers, etc.
Hopefully some of those ideas help!