Many years ago, when I was touring Israel with a group, we were going to visit Ben Gurion's residence on Kibbutz Sde Boker. While discussing the upcoming visit with a friend, I said the word בוקר boker with the accent on the first syllable, as in the Hebrew word for "morning". He corrected me and told me that the accent should be on the second syllable - which makes it the Hebrew word for "cowboy". What is the connection between the two terms?
Apparently, the original meaning of the root בקר is "to cleave, to split" (and is related to the similar בקע). Boker meaning morning derives, according to Klein, from "the breaking through of daylight".
As far as boker meaning cowboy, the root is in the Hebrew word for cattle, בקר bakar. I had always assumed that bakar got its name from the cloven hooves (which make them kosher.) However, from all the sources I've seen, the word actually derives from the function of the animal; as Klein defines - "the plowing animal".
As a verb, בקר means "to examine, to scrutinize, to criticize." This leads to two very similar nouns: bakara בקרה - control, and bikoret בקורת - inspection. Even native Hebrew speakers have difficulty distinguishing between the terms at times, and this site tries to point out the differences.
Lastly, בקר can mean "to visit", as in bikur cholim ביקור חולים - "visiting the sick". At first glance, perhaps nothing seems more Jewish than having the same root mean both "visit" and "criticize". However, according to Even-Shoshan, this sense of the word appears only once in Tanach, in Tehilim 27:4 --
only that do I seek;
to live in the house of the Lord
all the days of my life,
to gaze upon the beauty of the Lord,
l'vaker לבקר His temple."