There is no right or wrong way in the method of creating a medieval persona for the SCA. The persona a person decides to adopt as their own can result from an attachment to a particular name, favored period of time, or even style of dress. One person may have their counterpart set in mind before hearing of The Society for Creative Anachronism; others may very well sit back and play a generic character as they gather information before deciding.
An important point to keep foremost in mind when creating a medieval persona, especially for the SCA, is to strive toward authenticity as much as possible. This is not to say you cannot mix and match: it is certainly permissible for a Viking woman from an earlier period of the SCA time frame to dress as a member of an Italian court set in a later time frame when attending any number of the various functions and galas. The authenticity spoken of here regarding a persona for the SCA is aimed more at the creation of names, clothing, and weapons.
Finding a name for a medieval persona can be a difficult task, especially if a time frame for the persona has not yet been established. The name will need to be one of a person who "could have" existed in a certain time period but is not allowed to be the name of a person who did exist. The chosen name is also not allowed to be a name taken from a work of fiction. The name Harold or the surname Godwinson may be used, but not together as that would indicate that you are portraying Harold Godwinson aka Harold II, the last Anglo-Saxon King of England. The name Arthur abounds within the SCA but there is nary an Arthur Pendragon (or any other version of the name as found in many fictional works.) Fortunately, there are many websites in existence that have a large directory of first and last names that have been thoroughly researched and documented as allowable in the SCA. There is much room for imagination in the creation of a surname for a medieval persona.
Clothing a medieval persona is another area that should be more in keeping with reality than imagination. Banish from mind any such notions as pirate wenches sitting about in scanty leather bodices and micro-minis or gladiator's rushing off to battle wearing little else but a loin cloth and sandals. Choices in clothing (style, color, fabric) during the Middle Ages were dependent upon wealth, station, and role in life. To stay true to a chosen persona in the SCA it is necessary to really look at the styles that were in fashion during the chosen period and for the chosen station. As with names, there are many websites that will provide authentic patterns of medieval clothing from those who have spent countless hours poring over historic documents and paintings and turned their skill in fibre arts to create worn garb based upon that research. The garb should (ideally) be created from fabric that was in use "in the good old days." Most commonly used were wool, silk, linen, and hemp - all still found in fabric stores today. It would be best, though, to avoid synthetic fabrics such as rayon, nylon, polyester, and the like.
Geographic location and time period often play the largest role when it comes to choosing a persona. This is also the area that can take the least amount of research as virtually everybody has had some education in history. Beginning to choose a medieval alternate in this manner makes it much easier to find and narrow down names and clothing styles that strike each person's interest the most. A cursory investigation will ensure that the persona desired will, indeed, fit into the era and location fancied.
If any person is still unsure of just who and what they want to play, there is no pressure involved. No shame exists in using your given name and loaner garb until you come to some decision. Once a medieval persona is chosen a person is still able to play and have fun with mixing and matching clothing, styles, fighting and so much more. What is the SCA, after all, but The Party? It is a time to have fun, change clothing styles as desired, be boisterous, and meet people as the Middle Ages are explored, researched, and expanded upon.