The first English dictionary of 1604 was not called a dictionary but a 'table alphabeticall' (sic). The word 'dictionary' did exist at this time in English, but it usually referred to books of Latin vocabulary arranged by subject or to bilingual dictionaries. The first Latin-English glossary called a 'dictionary' was written by Sir Thomas Elyot in 1538. It was only during the 17th century that the word 'dictionary' began to be applied to books which explained the meanings of English words.
Early Latin-English glossaries or dictionaries were called by other Latin names apart from dictionarius or dictionarium. There was the Medulla Grammatice (marrow of grammar), Ortus Vocabulorum (garden of words), the Promptorium Parvulorum (children's repository), the Catholicon Anglicum English catholicon) and Alvearie (beehive). Other general words used to describe these glossaries were the Latin abecedarium (the English equivalent, described as obsolete by the OED, is abecedary), wordhoard, a word that existed in Old English) and vulgaria (Latin for 'vulgars').
After Cawdrey's Table Alphabeticall of 1604, we have John Bullokar's An English Expositor (1616), Thomas Blount's Glossographia (1656), Edward Phillips' The New World of English Words (1658) and the 1689 work Gazophylacium. The most famous dictionaries (Johnson's and the OED) called themselves dictionaries.
My favourite synonym of 'dictionary' is the now obsolete 'Richard Snary', which is a dictionary personified (Dick Snary sounding like a pun on the word in the 17th century). For more on this see World Wide Words.