I am trying to find out information for an Arzula Hokum and am running head-first into issues with her name. Her first name sounds like Ursula and her last like some variant of Holcomb(e). How do I know if a given Ursula Holcomb (or some permutation thereof) is the Arzula I am looking for, or if I have run into someone completely different?
I would treat each of Arzula Hokum and Ursula Holcomb(e) as separate people until some other criterion (i.e. other than the personal name) suggests they are the same person.
I expected to see a suggestion for using 'persona' here since it's one of those cases where multi-level person could be used to build-up a picture of the two individuals, and tentatively merge them with a higher-level persona.
I had a similar case to this myself where a Bertram Smith and a Benjamin Smith looked like they might be the same person. I kept the pieces of evidence for each individual separate until I was able to establish the connection - the probate calendar of England & Wales listed them both as aliases of the deceased.
Briefly, you have to look at other evidence to see if you can reject the same-person hypothesis. The more independent sources you can find that match, the more likely the two names are two refer to the same person. When seeking corroboration, make sure that your sources are truly different, rather than restatements of the same fact.
Spelling variants are quite common when dealing with older records. You should expect to do this kind of sleuthing more often than not.
You gather as many records/facts/evidence/personas as you can that may refer to the persons you are interested in. Then you evaluate all the facts in their entirety. Then you use your own judgement in deciding which of the records actually refer to the persons you are interested in. This is the basis of all research. You collect data. You evaluate it. You make conclusions that best fit the facts as you interpret them.
There are times when genealogical research is about understanding the nature of the space-time continuum.
When you identify a possible Ursula, then you must ask "Is it possible that Arzula could have been at that place at that time?". Do you have other (compelling) evidence that the person you are seeking was living somewhere else, or married to another person, or a different age. If so, you have good grounds to discard that candidate.
Of course, there will be cases where it is possible, but unlikely, that your target could be at that place at that time. Then you need to seek further independent evidence.