Siegfried Giedion seems to be the more common spelling, and it's generally a good idea to pick the spelling that is better established.
Still, you should probably note that there are two spellings, either in the index or as a footnote. For indexes in particular, the Chicago Manual of Style, 16th Edition, in the section on Indexing Proper Names and Variants, has some guidance:
16.32 : Choosing between variant names. When proper names appear in the text in more than one form, or in an incomplete form, the indexer must decide which form to use for the main entry and which for the cross-reference (if any) and occasionally must furnish identifying information not given in the text. Few indexes need to provide the kind of detail found in biographical or geographical dictionaries, though reference works of that kind will help in decision-making.
16.33 : Indexing familiar forms of personal names. The full form of personal names should be indexed as they have become widely known. (Any variant spelling preferred in the text, however, must likewise be preferred in the index; see 16.29.) Note that brackets are used in the following ex- amples to distinguish Chicago's editorial glosses from parenthetical tags such as those in some of the examples elsewhere in this section, which would actually appear in a published index.
Referring back to 16.29 (Style and usage in the index relative to the work):
Each index is a tool for one particular work. By the time the index is prepared, the style used in the work has long been determined, and the index must reflect that style. If British spelling has been used throughout the text, it must be used in the index. Shakspere in the text calls for Shakspere in the index. Hernando Cortez should not be indexed as Cortés...The use of accents and other diacritical marks must be observed exactly as in the text (Schönberg not Schoenberg).
The nice thing is that most of the time, you will simply be referring to him by his last name, 'Giedion,' thus eliminating the need to repeatedly choose. For the first mention, I would suggest either using parentheses:
"Siegfried Giedion (sometimes spelled Sigfried)..."
Or adding an asterisk and writing something to a similar effect in the footnote:
It should be noted Giedion's first name has also appeared as Sigfried in some publications; I have chosen the more common spelling.
The one thing you should not do is refer to him as "Siegfried/Sigfried Giedion" in every single case.
