Entry in progress—B.P.
 
Other early nicknames of the New York Yankees include “Hilltoppers,” “Invaders” and “Porchclimbers.”
 
Joseph W. Gordon, president of the club from 1903 to 1907. 
James R. “Jim” Price (1870-1929)
     
Wikipedia: New York Yankees
The New York Yankees are an American professional baseball team based in the New York City borough of the Bronx. The Yankees compete in Major League Baseball (MLB) as a member club of the American League (AL) East division. They are one of two major league clubs based in New York City, the other being the New York Mets of the National League. In the 1901 season, the club began play in the AL as the Baltimore Orioles (no relation to the modern Baltimore Orioles). Frank Farrell and Bill Devery purchased the franchise (which had ceased operations) and moved it to New York City, renaming the club the New York Highlanders. The Highlanders were officially renamed the Yankees in 1913.
(...)
Move to New York: the Highlanders years (1903–1912)
The team’s new ballpark, Hilltop Park (formally known as “American League Park”), was constructed in one of Upper Manhattan’s highest points—between 165th and 168th Streets—just a few blocks away from the much larger Polo Grounds. The team came to be known as the New York Highlanders. The name was inspired by a combination of the team’s elevated location in Upper Manhattan, and to the noted Scottish military unit The Gordon Highlanders, which coincided with the team’s president Joseph Gordon whose family was of Scots Irish heritage. Newspapers initially called the team “Gordon’s Highlanders” (e.g. New York World, April 15, 1903), which soon became just “Highlanders”.
   
Wikipedia: Gordon Highlanders
The Gordon Highlanders was a line infantry regiment of the British Army that existed for 113 years, from 1881 until 1994, when it was amalgamated with the Queen’s Own Highlanders (Seaforth and Camerons) to form the Highlanders (Seaforth, Gordons and Camerons).
 
Wikipedia: Hilltop Park
Hilltop Park was the nickname of a baseball park that stood in the Washington Heights neighborhood of New York City. It was the home of the New York Yankees of Major League Baseball from 1903 to 1912, when they were known as the “Highlanders”. It was also the temporary home of the New York Giants during a two-month period in 1911 while the Polo Grounds was being rebuilt after a fire.
 
The ballpark’s formal name, as painted on its exterior walls, was American League Park. Because the park was located on top of a ridge of Manhattan Island, it came to be known as Hilltop Park, and its team was most often called the New York Highlanders (as well as the Americans and the Yankees). This “Highland” connection contrasted with their intra-city rivals, the Giants, whose Polo Grounds was just a few blocks away, in the bottomland under Coogan’s Bluff.

Hilltop Park sat on the block bounded by Broadway, 165th Street, Fort Washington Avenue, and 168th Street. (...) Hilltop Park was demolished in 1914.
 
Baseball Reference
New York Highlanders
The New York Highlanders were an American League baseball team that played from 1903-1912. In 1913, the became known as the New York Yankees.
 
History
The new ballpark for the new team was constructed at 165th Street and Broadway in Manhattan, one of the highest points on the island. Formally known as “American League Park”, it was nicknamed “Hilltop Park” or “The Hilltop”, and was signficantly smaller than the Polo Grounds, the Giants’ home just a few blocks away. Publisher William Randolph Hearst’s New York Evening Journal referred to the new club as the “Invaders” in 1903, but switched in the spring of 1904 to the name that would stick for several years: the New York Highlanders. The name was a reference to the team’s location and also to the noted British military unit The Gordon Highlanders, which fit as the team’s president from 1903 to 1906 was Joseph Gordon. By 1904, the team was also being called the “Yankees”, a synonym for “Americans”, but initially “Highlanders” was the most common unofficial nickname of the new team.
 
Old Fulton NY Post Cards
3 April 1903, New York (NY) Press, pg. 4, col. 4:
Atlantas Finally Manage to Count Against Gordon Highlanders, Who Take the Game, 12 to 4.
 
Old Fulton NY Post Cards
6 April 1903, New York (NY) Press, pg. 5, col. 2:
HIGHLANDERS OR ISLANDERS?
Dispute About Name for Gordon’s Team, with Reference to Rivals.
“I see they’ve landed on the Island all right,” said the Fat Fan as he stood on Washington Heights and listened to the blasting of the rocks on the new grounds.
 
“Sure,” said the Elongated Enthusiast. “Why, you couldn’t have kept ‘em off with a whole battery of batteries. They look like a fine bunch, the Islanders do.”
 
“The which?” demanded the Fat Fan.
 
“Islanders—I-s-l-a-n-d-e-r-s—Islanders!”
 
The Fat Fan shook his head. Plainly he didn’t see the appositeness of the title.
 
“Where’dje get it?” he asked.
 
“Right here,” retorted the Elongated Enthusiast, waving his hand to embrace all the surrounding country. “Didn’t Brush do his best to keep ‘em off Manhattan Island? And haven’t they grabbed their slice of little old Manhat right under his nose? They’re the Islanders, sure.”
 
The Fat Fan didn’t seem convinced by this logic.
 
“Highlanders is the name,” he said, with deep firmness. “Ain’t this pretty near the highest spot in town? And ain’t Gordon the boss of the team? And isn’t there a world-beating crowd across the pond that they call the Gordon Highlanders? There’s the name for you—fits like the cover on a brand-new ball. That team’s going to be called the Highlanders.”
 
“Islanders!” retorted the Elongated Enthusiast, with deep conviction.
 
“Highlanders!” snapped the Fat Fan.
 
There were signs of anger in the air, but the sad climax of a fight between the baseball lovers was happily averted. A man who had overheard their argument stepped up and said:
 
“Excuse me, friends—just a minute—but what are you going to call the people down there?”
 
He waved his hand toward the Polo Grounds far beneath them. The Fat Fan and the Elongated Enthusiast looked at him in commiseration. Then they gazed at each other and grinned.
 
“Why,” said they in a breath, “they’re the Lowlanders!”
 
“Right,” said the third man. “But I’ll tell you how to settle that other name. You fellows think Griffith’s men are going to land near the top, don;t you?”
 
“Yep.”
 
“Well, then, they’ll be the High-landers.”
 
And the others agreed the name was likely to stick.
 
Chronicling America
15 April 1903, The World (New York, NY), pg. 8, col. 6:
GRIFFITH’S MEN ARE “GORDON’S HIGHLANDERS.”
Appropriate Nickname Has Been Suggested for Invading Americans.
(Same story as above.—ed.)
 
17 April 1903, Buffalo (NY) Commercial, “Baseball Brevities,” pg. 8, col. 1:
The name of Gordon Highlanders is suggested for the New York Americans. Mr. J. B. Gordon is president of the club, and the grounds are located on Washington Heights.
   
25 April 1903, The Sporting News (St. Louis, MO), “Pleased Patrons,” pg. 3, col. 2:
INTEREST IN HIGHLANDERS.
The Highlanders will have to play pretty fast ball if they expect to wean many people away from the home of the Lowlanders.
 
Newspapers.com
2 May 1903, Garnett (KS) Evening News, “The World of Sport,” pg. 2, col. 6:
New York baseball fans are having a hot argument over the relative merits of “Highlanders” and “Islanders” as nicknames for the new American League club. Why not compromise on Ighlanders?
 
21 August 1910, The Enquirer (Cincinnati, OH), “Nicknames of the Big League Teams,” sports sec. sec. 3), pg. 3, col. 2:
The New York American League team was named the “Highlanders” by James R. Price, sporting editor of the New York Press, when the Johnson organization entered the metropolis in 1903. The President of the club at that time was Joseph Gordon, and the grounds were on high land. In Scotland there is a regiment called Gordon’s Highlanders, and the combination of Gordon and the high land on which the team played suggested the name after the Scotch regiment.
 
In a letter to President Frank Farrell that was published in many newspapers on January 16, 1913, Chance wrote “Wouldn’t it be a good idea to call our team the New Yorks instead of the Highlanders, Yankees, Hilltops, Hillmen or Kilties? McGraw’s men have a copyright on the nickname Giants, and they deserve it, for they have accomplished big things in the National League. They always will be Giants in the full sense of the word. “Therefore, in calling our team the New Yorks we are not appropriating something that doesn’t belong to us. The nicknames ‘Highlanders,’ ‘Yankees’ and others are meaningless. In cities outside of New York they attract no attention. In fact, I think that this nickname business in baseball has been overdone. We are going to try to bring New York to the top of the heap in the American League, and we will have ‘New York’ on our uniforms. I hope the newspapers and the baseball public will call us the New Yorks in the future; also that we will be worthy of the name.”