The eagle on top of the parish church

As far as I can gather an eagle hs nothing to do with the name
There have been several suggestions as to the meaning of Eaglesham, one being that the placename is composed of the Old English pre-7th-century personal name Ecgwulf, ecgel meaning sword-wolf, and ham meaning village or homestead, one of the most common elements found in English placenames. Another explanation is that Eaglesham means kirkton or church town, derived from the Gaelic eaglais meaning church and, again, the Saxon ham meaning hamlet or village, an explanation which is currently being popularised by the Christian community in the village.
Campbell