It is ancient wisdom that names hold power. But for the modern neopagan they can also be a source of much confusion and distress. This mainly stems from what I've termed the 'authenticity dilemma'. In a nutshell, we borrow elements from distant cultures, far removed in time and/or space, yet their distance means we can never be sure of how they were originally understood or worshipped.
This shouldn't really matter. The pagan world was, by its nature, quite syncretistic. The history of religion and myth is littered with examples of deities being supplanted, combined, and reinvented. In most instances there simply is no single, authentic version. Unless you're interested in a strict reconstruction of a historical practice (and I kinda feel sorry for anyone who is, making any kind of sense out of historical pantheons is no easy task), this chould be viewed as license to make whatever you will of your deities. But sometimes it is easier said than done.
Below I'll briefly discuss some possible approaches to deity names, and problems related to them.
In a system with a relatively small number of deities, names aren't really necessary. A good example is Wicca, with its Goddess and God. Yes, many authors associate specific mythological names with these figures, but such things are always a personal choice, and by no means necessary. They only reflect a certain aspect of the deities, which are far more universal and archetypal in nature.
But we seem have a need to define things, to name them. It's human nature. We need to personify, and identify. Impersonal labels, while they may help break loose of the restrictions posed by identifying too closely with well defined, and therefore finite, figures, may begin to feel too, well... impersonal.
Names as Titles
You could take the stance that, while you may use a certain name for a deity, your deity is not, strictly speaking, the same one that was worshipped in antiquity. The name is merely a description of certain aspects of the deity, a convenience. The deities many neopagans worship are archetypal figures that draw influence from antiquity, but are defined by our modern understanding of the world and the human psyche.
Often deity names are, in fact, mere descriptive titles, when the etymology is clear. Bríd (or Brigid), for instance, simply means 'high one' or 'exalted one'. The etymology of Cernunnos is somewhat uncertain (according to Wikipedia), but it may simply mean 'horned one', from Gaulish karnon, 'horn'. Also, in addition to the names proper, descriptive epithets were commonly associated with classical deities. Such descriptive names may be the best choices if you want to keep your deities more... 'neutral'.
The danger, however, is that as much as you try to think of a deity as your own, you may start to identify it with its ancient namesake, studying its mythology and drawing more and more influence from there, which may in turn restrict your views of it, and lead you back to the doubts caused by the 'authenticity dilemma'.
In antiquity, deities absorbed aspects of other deities all the time. It was also common to refer to the gods of other cultures by domestic names, simply picking the deity name that seemed to fit best.
Modern neopaganism, and perhaps Wicca in particular, takes this phenomenon to an extreme. The Goddess and God obviously display aspects of many historical deities, and are frequently referenced by various names from mythology.
Regularly referring to a deity with the names of more than one historical counterpart may help to avoid overly identifying with a single mythological figure and thus restricting one's view of it, by way of emphasizing the nature of names as just 'titles', as considered above.