This does look like a name sign to me too. 
The list of public roads in Edinburgh [1] shows 4 entries for Easter Hailes Gate referring to the cycle route, although this not very conclusive as it refers to 'from opposite Newmills Road, Balerno' and 1 Lanark Road which is the old car showroom by the canal aqueduct ... more research needed 
https://www.edinburgh.gov.uk/directory/search?directoryID=10231&showInMap=&keywords=easter+hailes+gate&search=Search  