It wouldn't surprise me in the least if Prince Philip himself rejected this idea in its entirety. Don't forget William visited him not too long ago, IMO to broach the topic of naming a possible son after him. *He probably retorted, in true Philip fashion, "they'll get us mixed up!"*
And a possible response to the idea from HMQ, who I imagine would want to honor Philip for his 60+ years of service to her and the country: "Well he won't live forever, now will he?"
Which leads me to believe that future children, born after Philip's passing, may indeed carry his name.
JMO.