I checked the Hampshire Burial Index for entries of these surnames between 1500 and 1650. This is what is listed, indicating that the spelling of a surname was indeed at the whim of a clerk . (There was no Jerram entry, by the way).

Stranger Jeram 1591 (Please note that 'stranger' usually meant foreigner; the word was used, for example, in connection with Walloons and Huguenots in 16th century Southampton and elsewhere)
Agnes Jeram 1594
Joan alias Rowd Jeram 1600
Robert Jeram 1591

daughter Hector Jerom 1636
wife William Jerom 1612
Alice Jerom 1593
Bridget Jerom 1588
Jeremy Jerom 1641
John Jerom 1583
Margret (sic) Jerom 1544
Robert Jerom 1544
William Jerom 1615

Alice, wife of Richard Jerome 1631
Father, servant to Paulet Jerome 1626
Hector Jerome 1639
Peter Jerome 1626
Robert Jerome 1627
Thomson (sic) Jerome 1626 (online Thomson is, but is perhaps an error; Thomas seems more likely)
William Jerome 1592

Apparently, Jennie Jerome, Winston Churchill's mother, descends from a Timothy Jerome (1688-1750), who emigrated America about 1750, probably from the Isle of Wight.