late 15c., begel, small type of hound formerly kept to hunt hares, of unknown origin, possibly from French becguele "noisy person," literally "gaping throat," from bayer "open wide" (see bay (n.2)) + gueule "mouth" (see gullet).
"opening in a wall," especially a space between two columns, late 14c. from Old French baee "opening, hole, gulf," noun use of fem. past participle of bayer "to gape, yawn," from Medieval Latin batare "gape," perhaps of imitative origin. Meaning "compartment for storage: is from 1550s. Somewhat confused with bay (n.1) "inlet of the sea," it is the bay in sick-bay and bay window (early 15c.).
"passage from the mouth of an animal to the stomach," c. 1300 (as a surname), from Old French golet "neck (of a bottle); gutter; bay, creek," diminutive of gole "throat, neck" (Modern French gueule), from Latin gula "throat," also "appetite," which is related to gluttire "to gulp down, devour," glutto "a glutton." De Vaan writes, "We seem to be dealing with an onomatopoeic formation of the form *gul- / *glu-." Compare Old English ceole "throat;" Old Church Slavonic glutu "gullet," Russian glot "draught, gulp;" Old Irish gelim "I devour."
<a href="https://www.etymonline.com/word/beagle">Etymology of beagle by etymonline</a>
Harper, D. (n.d.). Etymology of beagle. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/beagle