It's worth noting that tarragon isn't a common ingredient in Filipino cuisine, so it's not surprising that there isn't a specific, widely used Tagalog word for it.
However, if you need to use it in a context where a more descriptive term is needed, you could use:
* "damo" (meaning "grass" or "herb") "na may lasa ng anis" (meaning "with anise flavor")
* "halamang gamot na may lasa ng anis" (meaning "herb with anise flavor")
These descriptions are more accurate and convey the taste of tarragon.