No do not think it is a different hand, the entry is fainter than other writing however if you compare the letters i.e. Capital L, y etc., they are the same hand.
Further confirmation is from the marriage entry again the image is on Ancestry
occ, residence Father
October 25th 1839 Thomas Shulver full age Batchelor Blacksmith Bedingfield John Shulver Labourer
Lucy Cook " " Spinster ----- " John Cook "
The name change appears to have taken place between 1841 and 1851 census, In 1841 her name is given as Lucy.