The use of Searle was discouraged for good reason. Searle took names from a variety of times and places and normalized them all to late period West Saxon spellings. This includes names from elsewhere in the Anglo-Saxon kingdoms, but also includes continental names. Sometimes the standardized forms are quite different from the documentary forms. As such, the spellings in this source are often forms that are not attested or even plausible given our knowledge of Anglo-Saxon sources.Tracking down the origin of the citation in Searle led to a collection of Anglo-Saxon charters known as Birch's Cartularium Saxonicum, where the name is recorded as Wifwyðe. The same charter is fortunately in the PASE database, and the name was able to be confirmed as being Wiswið. Commenters were unable to find any evidence at all of -with as opposed to -swith as a deuterotheme. Therefore, we have changed the given name to Eoswyth in order to register it.
In general, then, a dated citation in Searle should not be understood to be evidence that the specific spelling is dated to that time (or to any time at all). However, it is evidence that a person with some related name (sometimes a cognate in a different language) was recorded in an Anglo-Saxon record at that time. As such, every effort should be made to find the dated form of that name.