Continental Germanic names beginning with the "is" element include
Isbrand, Isabert, Iseger, Isigildis, Isohard, Hisburg, Isuwarth and others. This element can also be commonly found in the extended form "Isan-". The continental Germanic equivalent of Old English "giefu" was "geba" or "giba". This is not rare as an initial element, but it is very rare as a second element. Förstermann mentions only Thiatgif (Theitkeba in Swabian), and feminine names Ottogeba and Wiligip as examples.
Looking at this from the Anglo-Saxon angle, the element "is" seems to be uncommon. PASE (
http://www.pase.ac.uk/jsp/index.jsp ) lists Isegod, Isulf, Iseweard, Iseard.
I think all this demonstrates is that there are a number of ways this hypothetical name could have been recorded. Maybe Isegifa if Anglo-Saxon and Isegeba if continental?