One possible approach, using Facebook Graph Api
would be to perform a search against the name for users objects and also retrieve their pictures, using API version 2.2
it would be a call like:
GET graph.facebook.com
/search?q=miles davis&type=user&fields=id,name,picture
This would retrieve id, name and picture object for a search on miles davis, first results as example:
{
"data": [
{
"id": "805353876185303",
"name": "Miles Davis",
"picture": {
"data": {
"is_silhouette": true,
"url": "https://fbcdn-profile-a.akamaihd.net/hprofile-ak-xfp1/v/t1.0-1/c15.0.50.50/p50x50/10354686_10150004552801856_220367501106153455_n.jpg?oh=XXXXXXXXXXXXXXXX&oe=XXXXXX&__gda__=XXXXXXX_XXXXXXXXXXXXX"
}
}
},
{
"id": "1572370603017419",
"name": "Miles Davis",
"picture": {
"data": {
"is_silhouette": false,
"url": "https://fbcdn-profile-a.akamaihd.net/hprofile-ak-xap1/v/t1.0-1/p50x50/1501761_1382020035385811_1384168153_n.jpg?oh=XXXXXXXXX&oe=XXXXXXXXXXX&__gda__=XXXXXX_XXXXXX"
}
}
}, ...........
The field is_silhouette
is false if the user has a profile picure.