I had a quick google and there is evidence that locals may have reffered to Seaton Delaval as simply Delaval.
According to the wikipedia page for Seaton Delaval there is a 19th Century folk song called the 'Blackleg Miner'.
"Oh, Delaval is a terrible place
They rub wet clay in the blackleg's face.
And around the heaps they run a foot race,
To catch the blackleg miner!
So divint gang near the Seghill mine.
Across the way they stretch a line,
To catch the throat and break the spine
Of the dirty blackleg miner!"
https://en.wikipedia.org/wiki/Seaton_DelavalAlso the family name of the gentry who owned the land was Delaval. According to this wikipedia entry they owned a mine.
https://en.wikipedia.org/wiki/DelavalSo I do think it's possible that locals simply called Seaton Delaval, 'Delaval'.
Funnily enough Rootschatters have been helping me trace someone, who probably isn't my relative as it turns out. However whoever this person is, she answered a census return as Segil and it seemed likely to me that this referred to Seg Hill which is around the corner from the area you are talking about. So it seems that pronunciation and interpretation of names does differ.