There are a couple of ways to find out which database you're using.
From the record found after searching the library website, the View It section of the article's record will tell you which databases hold an article. You have to choose which database to access before you can see the article, so make a note of which one you choose.
e.g. This particular article is housed in three different databases: Academic OneFile, CPI.Q., and Literature Resource Center
If you're already in a database reading the article, the database name is often identified at the top left of the page. Note that PDFs are sometimes missing this information.
e.g. This article from the journal Nurse Education Today was accessed in the ScienceDirect database.
If it is ambiguous or says something like "searching 12 databases", enter the name of the database provider (e.g., ProQuest, EBSCO, etc.) as the database.