Good question! In the original story he was supposed to represent greed, big industry and well capitalism as a whole. Who he was or is doesn’t matter as much as it once did. (haha, get it?) I haven’t done a ton of research into Dr. Seuss is and why he wrote what he wrote or named him that way, and now I really want to look more into it. (If there is much more information on that than what I know!)
The 2012 movie of course took a new direction with him. He had a face, a personality, he was more human overall. He had reasoning for what he did and we had a bit of a look on what his family life was like. The movie still leaves several questions unanswered, one of those being his real name. The name Once-ler was used as a family name in the older movie, and if that is his last name, what is his first? You would think since we know so much about him now in this movie, that we would have a name. We are hearing things based off of what he told Ted, so maybe he wanted to keep that information from him. After everything that happened, it really it doesn’t matter anymore, does it?
I believe a few other blogs have talked about this in the past, while doing a bit of research I found this post.
I liked that perspective and that is about what I think on the matter. I think it would be nice to see fans make first names for their own Once-ler Ocs! Or their own headcanons on what his name would be.
Personally, I always just reference him as the Once-ler in my fanfictions because I can’t think of a name I would give him. I’ve seen some people call him Ed like his voice actor Ed Helms or having his name be Ted as well (for those who support the theory on him being the Once-ler’s grandson, it could be just passed down?)
As for what -ler means can depends on the language. I think this one fits the most
“-ler (v-v?, truncative?)has begun to [verb], is about to [verb], is in the process of [verb]ing“
which is Greenlandic
Source , which also has some other definitions for it.
By that definition above, Once-ler can mean was once doing or something similar. It seems a bit fitting for the situation.
I am SOOO sorry this was so long, I hope I was able to answer your question!!