Foreign key in MySQL

I am learning about database, I need to know something about the foreign key in MySQL.

Consider the following two tables.

1. UserGroupType.
2. UserGroup.

UserGroupType:

UserGroup:

In this table the foreign key is defined as follows,

foreign key (GroupType_id) references UserGroupType(GroupType_id)

I just want to know whether the name of the field in UserGroup can be changed? consider the following altered statement.

GroupType:

foreign key (Type_id) references UserGroupType(GroupType_id)

Is it necessary that both the field names must be same?

How to set the default value for datetime?

Thanks in advance, sorry if it is very basic things.

foreign key would have a different name from the primary key it is referring to, but necessarily , their data type and other attributes should be the same.
for example , if one is INT(10) unsigned the other should be defined the same.

but sometimes it is a good practice to name them similarly in complex queries. for example when you want to JOIN the relating tables, you can use the syntax :

userGroupType INNER JOIN userGroup USING (GroupType_id)

instead of :

userGroupType INNER JOIN userGroup ON userGroupType.GroupType_id = userGroup.GroupType_id