It's a point of scholarly debate as to whether or not Bottom's name simply refers to his occupation as a weaver or if it has more derogatory connotations. Scholar Cedric Watts of Sussex University points out that the Oxford English Dictionary states that in Shakespeare's time the word bottom was not used to mean "buttocks, backside," or even the more derogatory term we use to stereotype the donkey and anyone who acts like a donkey, which is ass or arse (as cited in "The Name 'Bottom' in A Midsummer Night's Dream"). Other literary critics interpret the name Bottom as only referring to the "bottom, or skein, around which yarn is wound," yarn used for weaving (eNotes, "Character Analysis: Bottom"). But Scholar Cedric Watts argues that both the OED and the literary critics are incorrect, that "bottom" certainly did mean backside in Shakespeare's days, and he uses all sorts of linguistic arguments as well as references to other Shakespearean works that indicate the same meaning to prove his theory ("The Name 'Bottom'").
If Watts is correct, then Shakespeare certainly is using the name Bottom to symbolize Bottom as the proverbial "ass." Bottom proves to be just as stubborn as a donkey, and even arrogant as well, in many instances. We especially see his stubbornness and arrogance in the scene in which Quince assigns the parts for their play. Bottom is so convinced of his own acting talents that he offers to take on the role of not just the lead Pyramus, but all other roles as well, including the lion that is meant to threaten Pyramus. However, his faith in his abilities as an actor proves to be absurd as we see him mess up his lines during rehearsal. For example, during rehearsal, he is trying to say a line intended to praise the smell of Thisbe's breath, but mixes the word "odours" with "odious," meaning "odorous," as we see in his line, "Thisbe, the flowers of odious savors sweet--" (eNotes, III.i.75). This word mix-up shows us that in reality, he simply isn't clever enough or knowledgeable enough to know what he is doing and saying. Even Puck recognizes his ridiculousness and his stubborn faith in his own abilities, and it is at this point when Puck decides to give him a donkey's head, symbolizing how Bottom is a proverbial ass.