I think George and Anne were the parents of John based on the details you provide, but the only source I have at present is familysearch, so I can't confirm everything for myself:
The 1713 marriage of John Plane and Ann Chapman at Teston is a good fit: it is on familysearch but that doesn't mention their parishes of Marden and Linton - I guess they comes from the PR?
Ann(e) Chapman looks like the one born at Marden in 1687 to Richard and Elizabeth (two of John and Ann's children seem to be named after them).
The children of Iden and Mary Plane at Marden were Mary 1721, Iden 1723, John 1724, Ann 1727 and John 1730. All these names are repeated in the children of John and Ann, tending to confirm that the fathers John and Iden are closely related.
The only child I can see for George and Anne is Anne baptised at Marden in 1688, which at least confirms they were there. I don't see the births of their children John and Iden on familysearch, but you must have a source for these?
Following your thought that the children of John and Ann could be named after relatives, this accounts for John, Ann, Iden, Richard, Elizabeth, Mary and George, leaving only Sarah, Robert and Thomas.
But only the children's' names Iden, Mary and George have any real bearing on the key question of which John married Ann Chapman, and the significance of these depends on the birth details of the brothers John and Iden.
Although Iden Plane was living at Marden around that time, three of his children, John 1724, Anne 1727 and John 1730 were buried at Linton in 1725, 1729 and 1733 respectively. I don't know what to make of that.
I would appreciate any details of the sources for the 1713 marriage at Teston and the births of John Plane and his brother Iden please. And in fact when and where was Iden born?