Pleonasm
noun 1 : the use of more words than those necessary to denote mere sense (as in "the man he said") : redundancy 2 : an instance or example of pleonasm
Does the overtalker in your life use more words than are necessary to denote mere sense? If so, you may rightfully accuse them of pleonasm. It's a word more than four centuries old, and it shares a satisfying final syllable with spasm and sarcasm, making it ripe for lobbing (good-naturedly, of course) at a friend. It comes from the Greek word pleonazein, meaning "to be excessive," from pleiōn or pleōn, meaning "more."
Logorrhea
noun : excessive and often incoherent talkativeness or wordiness
Perhaps the expressions of the overtalker in your life are of a more noisome type. If so, the word logorrhea may be just the thing, what with its second element being familiar to most of us only in a term we typically associate with stomach bugs and food poisoning. Logorrhea is of late 19th century vintage, plucked from New Latin, which is the Latin that's been heavily raided for scientific description and classification in English since the end of the medieval period. The logo part of course means "word."
Verbose
adjective 1 : containing more words than necessary : wordy also : impaired by wordiness 2 : given to wordiness
Those people among us who are prone to use more words than necessary are properly described as "verbose." The things those people produce with their words—replies, orations, and the like—are likewise properly accorded the same designation. Verbose has been with us since the late 17th century and has its origin in the Latin word verbōsus, from verbum, meaning "word," and -ōsus, meaning "full of." It also comes in a slightly longer noun version as well: verbosity, as in "the verbosity of a verbose reply."
Prolix
adjective 1 : unduly prolonged or drawn out : too long 2 : marked by or using an excess of words
Prolix may have the crisp efficiency of a good 21st century brand name, but the word is long established and of a classical origin: borrowed into English from Anglo-French and Latin during the period known as Middle English, its ultimate origin is Latin prolixus, meaning "extended." That word is formed from pro-, meaning "forward," and liquēre, "to be fluid."
Motormouth
noun : a person who talks excessively
When motormouth entered the language in the mid-20th century (near the dawn of the era of muscle cars) it was following in the footsteps of loudmouth ("a person given to loud, offensive talk") and blabbermouth ("a person who talks too much" and especially "a tattletale"), the earliest known evidence of which date to the second and fourth decades of the 20th century respectively. Smart-mouth ("one given to making remarks that aim for cleverness and wit but that strike others as cocky or annoying") followed about a decade later.
Garrulous
adjective 1 : given to prosy, rambling, or tedious loquacity : pointlessly or annoyingly talkative 2 : using or containing many and usually too many words : wordy
Garrulous in English dates to the early 17th century, but it enjoyed a literary heyday in the 19th and early 20th centuries, appearing in the works of the likes of Charles Dickens, G. K. Chesterton, P. G. Wodehouse, Anne Brontë, and Herman Melville. It's Latin in origin, coming from garrīre, meaning "to chatter, talk rapidly," itself probably coined in imitation of the sound of someone chattering.
Periphrasis
noun 1 : use of a longer phrasing in place of a possible shorter form of expression 2 : an instance of periphrasis
"Out with it, already!" one might say to another who tends to talk around the point instead of getting to it. The thing you're objecting to can be termed periphrasis, a word that is Greek in origin, from peri-, meaning "around," and phrazein, "to point out." Periphrasis can be contrasted with a related word: holophrasis refers to the expression of a complex of ideas by a single word. Both are also related to antiphrasis, which refers to the usually ironic or humorous use of words in senses opposite to the generally accepted meanings, such as in a phrase like "an ancient creature 2 days old."
Circumlocution
noun 1 : the use of an unnecessarily large number of words to express an idea 2 : evasion in speech
There's no way around it. Or maybe there is. Circumlocution is firmly in the second camp. While the word first referred to the use of many words to express an idea that could be expressed in many fewer, it has also for a long time referred to evasion in speech. Its origin is Latin: circum-, meaning "around," and locutio, meaning "speech."