Transactional Replication - Publications with same Name on the same Domain
Yes, it is fine to have same publication names on as many different publishers as you want.  You most likely can't have dup publication names on a single publisher though, but that is not what you are asking.  Further, you can easily test this out in your test/dev environment, on two servers.  Create a single pub/dist/sub server, and on second server, create another pub/dist/sub, and on each, create a publication with same name.

About your comment "but in the past I've found replication to be "problematic" - please explain?