Money invested vs increased valuation I am looking for a name and historical data for a concept. I think it is easiest to explain by example. Consider stock in XYZ Inc worth \$10 per share and there are 10 shares, so the market cap is \$100. I really want to buy a share, but the current owners are happy with it so I have to pay \$11. So I have added a new dollar to the stock ecosystem, but now the market cap is \$110. That means there are \$9 of new value that have appeared out of thin air.
Is there a name for my $1 that I added and the \$9 of new created value? Is there a name for the ratio of the two?
I am curious about these values because I suspect the ratio has been abnormally high for the stock market at large since the Great Recession. In other words, the value of the total stock market has outpaced the amount of new money invested in the stock market.
Is this suspicion accurate? Does anyone track this data?
I don't know the name of the term you are looking for but the ratio you are looking for can be calculated as the volume of trade data is usually available for each stock. A similar metric that you may like is Volume-Weighted Average Price which takes into account the volume of trade.

Is this suspicion accurate?

It's very subjective but your suspicion seems to be based on your hypothetical construct which needs further discussion. You say 'I really want to buy a share..'. Now why would that be? For a rational investor, it will be when she sees it's value to be \$11 rather than market value of \$10.
When enough investors are there in the market that think that the value of the share should be high then the price of the stock goes up (and there's nothing wrong with it), which reflects, in a way, the collective sentiment about the stock.
In the above reasoning, we consider the market as a non-cooperative non-atomic game, in which single player's decision has no influence on market outcome. Therefore, an individual is not pushing the price of the stock but rather the general consensus that the stock is going to giver higher returns.
So your suspicion is correct when these at least one of the following assumptions are not be valid: (a) investors are not rational (domain of behavioral finance); (b) game cannot be considered non-atomic (there are big players that can alone move the market - almost always true); and (c) there is collusion among investors to bid the price of a stock up.
So yes, for some stocks, to some extent it is perfectly possible that some investors bid the price up to the level that it doesn't reflect the real valuation. This is more common with penny stocks which is why there are more restrictions/regulations around them.