Sometimes, this can be a bit like making a jigsaw puzzle. For example, I have two characters from the one family who have been in quite a few stories. These are Rory, who was born in the 1930s, and his grandson Duffy, who is in his forties in his main story, but who appeared as a youngster in someone else's story. His two sisters are mentioned, but his parents weren't named.
In writing Rory's story, I had to think about names for Duffy's parents. His father is now named Davey, and he appears as a small child in the early part of a book called The Red Cat. However, his mother was just a name... Then I needed to work out the provenance of another character whose name was (provisionally) Penny. I checked my timeline and realised "Penny" would be about two years older than Davey, and that they could very well have met through a third character named Magda. So... maybe "Penny" could become Davey's wife and the mother of Duffy and his sisters?
There was a problem though. The grown-up Duffy has a wife named Pen, and it seems unbelievable that he wouldn't have remarked on the coincidence when he and Pen were courting... "How odd! My mum is called Penelope too..." So, I decided that, if I go ahead with this plot-line, "Penny" needs a name change. Since she was born in 1951, I needed a name that would work for the period, and which would fit the surname she has to have, and also fit her personality, which I had established. I wanted to keep the initial P for other reasons already lodged in the story.
The names I considered, which would have the same "feel" as Penny were...
Peggy - I like that, but it doesn't quite match the personality.
Pepper - Probably too modern.
Petal - Doesn't work with the surname, which begins with L.
Petra - Too much like an existing character's name.
Pansy - Too soft.
Polly - I like that, and it was a strong contender.
Poppy - as with Polly.
Patty - I like that too, but maybe a bit soft.
Pom - Another strong contender, being derived from Pomegranate (which may be a bit too odd for 1951.)
Pixie - I really liked that, but it doesn't work for plot reasons.
Pippa - Too close to an existing character.
Patra - I liked that, but a bit the same as Petra.
Patina - Another one I liked.
Perry - Already in use for another character
Persephone - with Percy as a short form. I already have a character who goes by Percy.
Pandora, with the short form Panda. This is the one I picked, because it works for the character. It is unusual, but not as odd as Pomegranate or Pegasus.
So there you are...