Alexander Wright baptism handwriting help - King Edwards parish

[Tom Wright]

Need some help deciphering the location name next to father William Wright and also the witness names.

Image removed

[Tom Wright]

Here is the image I need help to decipher.

[goldie61]

Witnesses Alexander Chalmers senior (Sen^r) and Alexander Chalmers junior (jun^r) in ? of Eden.

The place given for William Wright looks like h?dy hill.
Can you find a place nearby with a name like that?
Where did the baptism take place?

Possibly both these are names of farms.

This a great site to find Scottish places
https://scotlandsplaces.gov.uk/places
You may have to do some searching backwards and forwards from the place you know the baptism took place.