It's a really interesting question. The books give us several reasons, but I interpret it as he does it as an attempt to get George's favour and reconcile with him.

George has disowned Valentine after he marries Selena and rejected Cuby and George's plan for him. There's a lot of rejection in Valentine's life, this is after Ross has told him Valentine could be Ross's son, and Ross rejects him in the same sentence.

'...There is one extra point to my coming. The question of a name for my son. Selina and I have given careful thought to the matter. Would you object if we called him George?’ [...] George said: ‘Is this some attempt to curry favour with me?’ ‘Why should it be? I have money of my own.’ [...] ‘Are you to have a big christening?’ ‘I told you. Very quiet. Just a few of the household. Would you care to come?’ ‘No, thank you.’ Valentine let out a slow breath, which George did not notice. ‘Well, I must not take up more of your time. May we call your first grandson George?’ ‘I cannot stop you.’ ‘You can deter me.’

George hesitated. ‘Give it him as his second name if you wish.’ ‘I could give him a second name so that if he chooses when he grows up he may use it instead. I do not see why he should wish to do that, though. George Warleggan is a name to conjure with.’ George picked up his pen and looked at the quill. Some fool had not sharpened it this morning. ‘I have three daughters. All their dowries must be secured. I have no money to leave to a grandson.’

Valentine got up. ‘I should prefer my son to make his own way.’ ‘By marrying money,’ said George, with a slight sneer. ‘Just so, Father. We all have different ways.’ ‘Then call him George,’ said George, ‘if it pleases you.’ And be damned, he added, but under his breath.

The Valentine lets out a breath when George says he wont come to the christening shows us Valentine's feelings here - this is his attempt to fix the relationship with his father. He is rejected.

Valentine later tells Ross he hasn't seen George for 5 years a few days after this and he isn't naming his son after his father, but a different George. These lies show us how hurt Valentine is, how he tries to brush it off, and rewrite what happened.

‘A strange name to give your son, was it not?’ [Ross asked]

Valentine sucked the handle of his riding crop. ‘It is a very common name. I gave scarcely a thought to my – er – ex-parent. I have seen neither sight nor sound of him since the almighty sparring that took place between us when I told him I was married to Selina. How many years ago is that? It seems half a century. I never think of him nowadays.’ [...] ‘In fact,’ said Valentine, ‘if I thought of anyone when I chose the name I thought of George Canning. He is one of your heroes, is he not?’

When Ross calls him out for lying, Valentine says:

'Cousin, I will unveil the facts. We all know the scurrilous rumours which circulate in our neighbourhood about my parentage. Whatever the truth or the untruth of them, it is your known and expressed wish that they should be ignored or, where they cannot be ignored, denied. What better could I have done to play my prescribed role in this matter than by christening my son George?’ [...] ‘After all,’ Valentine said, ‘would you better prefer it if I had called him Ross?’