Does Merkle Tree root hash changed when miner node not found POW nonce? In bitcoin PoW process,if miner does not found the nonce, I understand that he must
to increase nonce and rehash the entire block header again
to mine the new block.
so if nonce defined 4byte[between 0 and 2^31],
goes from 0 to 2^31 finally and even not found the target hash, does the miner rehash the Merkle Tree including coinbase transaction?
And what algorithm for miner to change coinbase transaction?
Not necessarily. If a miner runs out of nonces, there are still other things in the block header he can change. The version number and timestamp can both be changed to effectively increase the number of nonces that can be tried. However there are not as many possible version numbers of timestamps that can be used as they have to fit within certain constraints.

If the miner does not change those, then he will change the merkle root. This is most commonly done by incrementing a value in the coinbase transaction known as the extranonce. This value is stored in the coinbase script where miners are free to place up to 96 bytes of arbitrary data. By incrementing the extranonce, the merkle root will change and the miner can continue with searching through nonces again.

If the miner runs out of nonces and extranonces, he can reselect transactions to be included or reorder transactions, both of which will also change the merkle root.