Yes, the major dialects of Serbo-Croat* are named after what word is used for who: što-, ča-, or 0kaj- kavian. However, those three divisions are all basically dialects of Croatian, not Serbian. Both standard Croatian and Serbian are based on the štokavian dialect.
The dialects also have a further classication: ekavian, ikavian, and ijekavian. These are names after how the old Slavic vowel jat/yat is pronounced. Ikavian dialects pronounce it as “i,” ijekavian dialects pronounce it as “ije/je” and ekavian pronounce it as “e.” Standard Serbian is stokavian/ekavian while Standard Croatian is stokavian/ijekavian (my previous example of mleko/mlijeko shows this difference.)
*There is a fourth dialect, Torlak(ian), that is sometimes included as major division of the Serbo-Croat dialect map. This is spoken in Southeast Serbia and is sometimes considered a dialect of Bulgarian. It’s interesting, as, like Bulgarian and Macedonian, it apparently has also abandoned the Slavic case system.