With respect, the simple "rename" option may not work. I tried it, and ended up being given lots of search results and hints in a tree which turned out to be the same tree I first created. Ancestry had evidently kept a copy!
I think, having had to split a large tree into manageable branches, that the best tactic may be to de-link the trees, get the FTM tree right (and with the right name), then delete the Ancestry version, and finally link / upload the FTM tree. This seems to work most smoothly.