Where does “さいたま” come from?

さいたま (Japanese) comes from Japanese 埼玉, from Old Japanese 埼玉, from Old Japanese 埼 — cape.

Ancestry of “さいたま”, step by step

Step	Language	Word	Meaning
1	Japanese	埼玉	{{w\|Saitama Prefecture}}
2	Old Japanese	埼玉	—
3	Old Japanese	埼	cape