If an atom is fully ionized by removing all electrons, is it still an atom? This is a question about terminology. To me, it's clear that the nucleus of an atom is still an atom. But a comment by Willie Wong at Is nature symmetric between particles and antiparticles? raises this question. Similarly, arguments go either way at the physics forums question: "is it possible for an atom to have no electrons?" http://www.physicsforums.com/showthread.php?t=50333 
 A: No, it's just a nucleus at that point, although we should admit that the distinction is semantics.  Because it is semantics, I look to other precedents and clearly find that it would not be consistent to call them atoms.  Consider the case of twice ionized Helium, $He^{+2}$.


*
*When the particle has high energy, moving among ordinary matter we call it an alpha particle

*When the particle has high energy among a sea of other high energy (disassociated) particles we call it part of a plasma

*When the particle has thermal energy among other disassociated particles with thermal energies... that doesn't make any sense, why would they be disassociated?

*When the particle is sitting by its lonesome in the middle of space, I would call it an alpha particle

It's pretty much impossible to ask the question without considering the context in which the nucleus/atom exists, but I can't think of a context in which it should clearly be called an atom.  So for the general sense, I would say it shouldn't be called an atom.
A: In most cases I don't see it behaving as "an atom" in any meaningful way (i.e. in most circumstances it is not going to engage in chemistry but in magnetohydrodynamics). 
Low energy may make an interesting borderline case.
A: If we are thinking of low atomic number atoms, as 
Zassounotsukushi  mentions, scientists use different names for the bare nuclei of atoms. Mainly, though,  because they were encountered as unknown entities in experiments and then identified with the nucleus of an atom. 
If we are thinking of the periodic table, it would be hard and confusing to come up with a different name for each electronless representative. I have not heard of experiments with stripped atoms with high atomic numbers, but presumably there exists such a possibility. Common sense dictates that an adjective should be found accompanying the periodic table name: "stripped iron" or some such.
After all terminology should reduce confusion not increase it.
