Thank you all for taking a look at this.
I'm glad other people think there is a difference in handwriting between the 'text' of the entries and the names signed.
So it could be the case that this is a copy of the actual signature of Robert Stainthorp, who I believe may have been my five-greats grandfather, the father of Francis Stainthorp (1765-1822).
What's odd is that on the Bishop's Transcript of the parish record entry for the marriage of Robert Stainthorp to Margaret Wilchinson on 15th May 1764 in Rudby, which I believe was probably the first marriage of the same Robert Stainthorp who later married Anne Porrit in Ayton, he evidently didn't or couldn't sign the register, as the transcript reads "Robert Stainthorp X his mark".
...so even if and when I get a look at the original P.R. for Rudby, I won't be able to compare the signatures.
Paul