Surprisingly this question can be answered with a simple word - Yep.
The LinkName is filled in by what you put inside of alias inside of the HTML. The caveat of it though is that if you put AMPScript inside of the alias tag, it will only display the AMPscript, not the final processed value.
<a href="..." alias="%%=v(@alias)=%%"> would return
%%=v(@alias)=%% as the LinkName.
The best workaround for this is to use a concat to build the alias attribute in the a tag. Like so:
<a href="..." %%=CONCAT('alias="', @alias,'" ')=%% >
but I seriously recommend always using a static value for alias wherever and whenever possible.