┌─────────────────────┐
  │                     │
  │    MySQL/mariadb    │
  │                     │
  └─────────────────────┘


==> If you enter to MySQL as normal user with this command (by entering the root password), everything is fine:
$ mysql -u root -p



==> If no...



######################################################
##########  CONFIG NEW versions of mariadb  ##########
	(debian 13)

# mariadb-secure-installation

	Enter current password for root (enter for none):  [ENTER]

	Switch to unix_socket authentication [Y/n]  n

	Change the root password? [Y/n]  y

	Remove anonymous users? [Y/n]  y

	Disallow root login remotely? [Y/n]  n

	Remove test database and access to it? [Y/n]  y

	Reload privilege tables now? [Y/n]  y

		Thanks for using MariaDB!


Now, if you enter to MySQL as normal user with this command (by entering the root password), everything is fine:
$ mysql -u root -p





######################################################
#######  CONFIG OLD versions of MySQL/mariadb  #######
	(debian 11, debian 12, ubuntu server 20 ...)


# mysql_secure_installation

	Enter current password for root (enter for none):  [ENTER]
	
	Switch to unix_socket authentication [Y/n]  n

	Change the root password? [Y/n]  y

	Remove anonymous users? [Y/n]  y

	Disallow root login remotely? [Y/n]  n

	Remove test database and access to it? [Y/n]  y

	Reload privilege tables now? [Y/n]  y

		Thanks for using MariaDB!


Now, if you enter to MySQL as normal user with this command (by entering the root password), everything is fine:
$ mysql -u root -p





######################################################
#########  CONFIG OLD OLD versions of MySQL  #########
	(debian 8, debian 9, debian 10 ...) 


# mysql -u root

	USE mysql;
	UPDATE user SET plugin='mysql_native_password' WHERE user='root';
	FLUSH PRIVILEGES;
	exit;



# systemctl restart mysql.service



# mysql_secure_installation

	Enter current password for root (enter for none):  [ENTER]

	Set root password? [Y/n]  y

	Remove anonymous users? [Y/n]  y

	Disallow root login remotely? [Y/n]  n

	Remove test database and access to it? [Y/n]  y

	Reload privilege tables now? [Y/n]  y

		Thanks for using MariaDB!



Now, if you enter MySQL as normal user with this command (by entering the password), everything is fine:
$ mysql -u root -p







########################################################
### Change MySQL admin password NEW mariadb versions ###

# mysql -u root

mysql> ALTER USER 'root'@'localhost' IDENTIFIED BY 'your_new_password';
mysql> FLUSH PRIVILEGES;
mysql> exit;




##############################################################
### Change MySQL admin password OLD MySQL/mariadb versions ###

# mysql -u root

mysql> SET PASSWORD FOR 'user'@'localhost' = PASSWORD('your_new_password');
mysql> FLUSH PRIVILEGES;
mysql> exit;




Or you can also try...

# mysql -u root

mysql> UPDATE mysql.user SET Password=PASSWORD('your_new_password') WHERE User='root' AND Host='localhost';
mysql> FLUSH PRIVILEGES;
mysql> exit;