I've had a look at the image. The Initial does look like the P in Patrick, and could only be an R if the bottom stroke is completely missing through being too faint - unlike the other Rs on the page (Richard, Robert) which are very clear. The Roberts, Richards and Rebecca on other pages could almost begin with B. It doesn't compare to the L of Lydia. I would say the second letter is an 'h' as it compares to that letter in 'Richard'. The next letter does look more like the other 'o' s on the page rather than most of the 'a' s. The last element looks like the 'ly' in 'Emily', but could also be 'by'.

Not much help I'm afraid.