If we turn to the Domesday Survey (1086) the name of the parish is spelt Soeham or Seaham, then at a much later time as Seham. In other manuscripts it is given variously as Soame, Shoame, Swoham, Some and Saham, and a charter mentions the town as Soegham.
Probably the earliest official mention of Soham was made in A.D. 972 concerning the grants of land at Rettendon, Soham and Ditton. "Soeg" is derived from the Anglo-Saxon word "sagt" meaning drenched.
These two words come from the root verb seen in Anglo-Saxon called "sigan" - to soak or drain. "Sigan" is also connected with the Icelandic word "saggi", meaning moisture or dampness, so it would suggest that Soegham was a culmination of two words, either drenched or soaked and hamlet and this would make sense considering the amount of water in the vicinity at that period.
Interesting facts about the Name / Word Soham in India
Soham is a fairly common name given to people in India meaning
'I am He'- the presence of divinity of each soul
Your first name of Soham makes you a quick thinker, both philosophical and creative. You appreciate music, art, and drama and, if given training, could excel in those fields. Self-consciousness may prevent you from feeling at ease in positions of impromptu expression. Desiring to be free from detail and monotony, you find it difficult to finish what you start if it does not hold your interest. You enjoy reading and the beauties of nature, experiencing peace and relaxation in outdoor activities. A very individual, independent person, you live within your own thoughts. With acquaintances and strangers, you tend to be reticent and reserved. Your friends never know whether they will find you friendly and charming or lost in introspection. When unhappy or disappointed, you can be moody and temperamental, feeling misunderstood and unappreciated. You will go out of your way to help others, and find it difficult to say "no" and mean it. Others impose on your generosity at times. You enjoy sweets and starchy foods. Over-indulgence could cause a weak back, skin conditions or arthritis later in life. The heart and lungs could also be affected at stressful times.
In India Soham has several meanings
Soham (Sk.). A mystic syllable representing involution: lit., "that I am".
Soham, a mystic syllable representing involution; (lit. "that am I.")
So'Ham, the reverse of Hamsa, symbolizing black magic. (sas, that; aham, I: I that very person, I myself -- expressive of bad egoism -- while Hamsa (aham, I; sas, that: I am That) is an affirmation of divine unity.)
Soham (Skt), "he (is) I"
Soham is also linked to Mantra yoga meditation practices
If the Mantra is Soham, the sound 'so' should be mentally intoned with the inflowing breath and 'ham' with the outflowing, in the same way as with Om. The sentiment or the contemplative part may be based on the affirmation: "I am one with the eternal spirit within and around. The self in me is of the spiritual nature of my soul, rather than a product of physical instincts and personality traits. The ego in me is purified by this communion with my soul, the essence of which is the same as the infinite, transcendental spirit of God, or the Self."