What will happen if bitcoin transactions became anonymous like Monero tomorrow? Will it increase the demand of bitcoin even more in the world ? Or will it have negative effect like government making restrictions on bitcoin ?
First of all, it can't magically become an anonymous from tomorrow, it's not like devs can change Bitcoin one day or make a fork and everyone will follow it. But since it's a hypothetical question, let's discuss it, no problem.
Nothing good will happen. First of all, there isn't demand on anonymity because if there was, then Monero would be the number one currency, not Bitcoin. Since Monero is ranked #29, it means that anonymity is not really what the majority of crypto users want. Also keep in mind that Monero isn't the most popular currency for making transactions.
To my mind, if Bitcoin becomes very anonymous one day, then it will have problem with the governments and they'll try their best to prohibit businesses from accepting Bitcoin payments, as they do with Monero today.