There is a difference between "Crack" and "Tell" when it comes to jokes. To crack a joke is to make an original witty remark (i.e. something that, in context, is funny, but would not necessarily stand alone as humor); to tell a joke is to relate a bit of humor that is expected to be received well by your audience.
A sample of the difference:
Your friend says "Hey, did you hear this news story? A bookie in Vegas was attacked by one of his customers."
You say "Wow, I guess they were really at odds with each other. Baaahaha!"
You have just cracked a joke. A small, lame pun-based joke, to be sure, but still.
Your friend says "How many mice does it take to screw in a light bulb? Two, but how did they get into the lightbulb in the first place?"
Your friend has just told a joke.
The earliest dog named Rover I found is in a 1718 list of common names for hunting dogs.
Etymology
Rover was a common name for a hunting dog in 1718, along with other names such as Bouncer, Fiddler, Gallant, Lively, Ranger, Ruffler, Soundwell, Trouncer, Traveller and Wonder.
The name is most likely from rover, n.2 in the OED, specifically sense 2a:
A person who travels from place to place without fixed route or destination, esp. over a wide area; a wanderer, a roamer; a nomad. Also: an animal which ranges over a wide area.
This is etymologically from the -er suffix applied to rove v.2, the first definition in the OED being:
To shoot at an arbitrarily selected mark, and senses deriving from this.
Etymology: Origin uncertain; perhaps a midland form corresponding to northern rave v.2, either as an analogical formation or as the non-northern reflex of a borrowing < the possible early Scandinavian etymon of rave v.2 (although this would imply a date of borrowing significantly earlier than either English word is attested).
On the other hand, the etymology of piratical rover, n.1 (cf sea-rover) is:
< Middle Dutch rōver or its cognate Middle Low German rōver reaver n. Compare Middle Dutch seerōver , Middle Low German sērȫver sea-rover n. and also Anglo-Norman roveres sur le mere , plural (1429 or earlier). Compare later rove v.1
1839
The boy's country-book (1839) by William Howitt features a happy dog called Rover:
1801
The school for children, or A selection of instruction and entertaining tales (1801) "from the French of" Vincent de Langres Lombard features a poem called "VERSES TO MY DOG, ROVER, WHEN GROWN OLD.":
And there's a song in The farmer's boy: a rural poem (1801) by Robert Bloomfield called "THE SHEPHERD AND HIS DOG ROVER":
Which was also printed in The Monthly mirror: reflecting men and manners (1801):
1780
A General Dictionary of the English Language (1780) by Thomas Sheridan may offer an etymology. The definition for ranger gives both "a rover" (presumably human) and "a dog that beats the ground" as synonyms for ranger. Perhaps ranger was first applied to "dogs that beat the ground".
1740
Poetical works (1740) by William Somerville (1675 – 1742) includes "The Officious Messenger, A Tale" which appears to feature a dog called Rover:
Ye world-makers of Gresham-hall,
Dog Rover shall confute you all ;
Shall prove that every reasoning brute
Like Ben of Bangor can dispute;
...
Rover, as heralds are agreed,
Well-born, and of the fetting breed,
Rang'd high,was stout, of nose acute,
A very learn'd and courteous brute.
...
With him obsequious Rover trudg'd,
Nor from his heels one moment budg'd;
...
The trusty Rover lay hard by,
Observing all with curious eye.
...
The servants, to the stranger kind,
Leave trusty Rover still behind.
...
Rover, who now began to quake,
As conscious of his foul mistake,
Trusts to his heels to save his life;
1718
It appears in a list of "Hunters' TERMS, &c" in The compleat sportsman (1718) by Giles Jacob, and is given as a common name for a hunting hound:
Best Answer
Some relevant articles: "Whose name is it anyway? Varying patterns of possessive usage in eponymous neurodegenerative diseases", by Michael R. MacAskill and Tim J. Anderson (2013), and "The synthetic genitive in medical eponyms: Is it doomed to extinction?", by John H. Dirckx (2001).
The abstract to the MacAskill and Anderson article says
Here is Figure 1, which presents the relevant results in graphical form:
The results summarized in this figure don't differentiate between different varieties of English. (Although PubMed is "developed and maintained by the National Center for Biotechnology Information (NCBI), at the U.S. National Library of Medicine (NLM), located at the National Institutes of Health", the database contains literature that was published in the UK as well as literature that was published in the US.) But there do seem to be notable differences in usage between American English and British English in this area. MacAskill and Anderson analyzed the use of "Parkinson's disease" vs. "Parkinson disease" in UK-based vs. US-based journals general journals and found evidence that the rise of the latter form in US-based journals was influenced by changing editorial preferences. It seems probable that the rise of "Down syndrome" had a similar cause.
A quick look at "Down's syndrome" vs. "Down syndrome" in the Google Ngram Viewer does support the point that has been brought up in comments about the ratio of "Down syndrome" to "Down's syndrome" being higher in the US than in the UK. However, both forms do seem to exist in both varieties of English.
American English:
British English:
Possible phonetic pressures for the change?
John Lawler suggested in a comment beneath the question that certain phonetic features of "Down's syndrome" may have contributed to its becoming less preferred relative to "Down syndrome":
This seems somewhat plausible, but the initial dominance of the spelling with 's, and the data in the MacAskill and Anderson article showing a parallel decline in the frequency of Gaucher's disease vs. Gaucher disease, indicate that a phonetic explanation is probably not the whole story even if it may have some applicability. While it seems hard to estimate exactly how much of a role phonetics may have played in the development of the spelling Down syndrome vs. other factors, I'd guess that other factors were actually more important.
Dirckx makes a similar suggestion on p. 19, saying