I can put some text into the player's "alias" attribute; but whenever I refer to player.alias into any script, it gives me the text it finds into the attribute player.pov_alias. How could I make it NOT override the main "alias" attribute? Besides setting the "pov_alias" attribute, I mean.

If you are playing as an object, its alias is the pov_alias.

You can set all sorts of things under the 'Player' tab:

< offtopic >
/me thoroughly investigates that screenshot.

There is a cave?! I did not find that yet =(

< /offtopic >

pov_alias is copied over the alias attribute when an object becomes the player. So you could either put the text you want into pov_alias, as KV suggested. Or you could change player.alias after the player object has been set; for example in the game's start script.
Or you could use player.external_alias, which contains the value that you originally entered in the alias box. (This is used so that if you allow the player to control a different character later on, it can restore the original alias)

If you want to switch player object during the game without pov_alias overwriting alias, then you could do that by temporarily removing the script game.changedpov. This probably isn't a good idea, though.

Thanks. I have to stick with pov_alias, I suppose.

it's also the same with the 'look' vs 'pov_look', as this confuses a lot of people:

they put in their description for their Object's 'look' String/Script Attribute, but since this Object is also a Player Object, they don't see that description and are confused, not realizing that while you're controlling that Object, it's using the 'pov_look' String/Script Attribute, and so they don't have any look description, but while NOT controlling that Object, they'll then see the look description

while controlling an Object, it uses the 'pov_NAME_OF_ATTRIBUTE' Attributes, and while NOT controlling an Object, it just uses the 'NAME_OF_ATTRIBUTE' Attributes.

so, for example, in the GUI/Editor, there's two locations for the look descriptions: under the 'setup' Tab (for when NOT controlling the Object) and under the 'player' Tab (for when controlling the Object)

for the 'look/description' Attributes:

Room Objects use the 'description' String/Script Attribute

Player Objects have (can use) both the 'look' (when NOT controlled) and 'pov_look' (when controlled) String/Script Attributes

(non-room and non-player) Objects use the 'look' String/Script Attribute