Well, maybe not specifically heroic for his military deeds, he was for his law enforcement - Sam Steele. Definitely famous here (how many folks get their own “Heritage Minute”)?
He was the first CO of the Lord Strathcona’s Horse fighting in the Boer War, and was for all intents and purposes an honorary Major-General of the Canadian Foces during WW1.
More here:
Washington
Lee
Grant/Sherman combo
Patton
Smedley Butler
He’s a bit of a national hero here in Israel, too.
Hmm, I’d think Scots pride would overlook Haig, when there are so many better candidates such as Chinese Gordon. Or the London Scottish Regiment, including Basil Rathbone, Ronald Coleman, Herbert Marshall and Claude Rains
How about the Animal Kingdom? Not just dogs, war horses, elephants and the experimental Swedish Moose; or when an animal was the casus belli such as the Pig War. But rather when non-domesticated animals intervened in human history on their own:
William III of England’s plans to invade Scotland died along with him after his horse stepped into a mole burrow. The Jacobins gratefully toasted “the little gentleman in the black velvet waistcoat.”
The Aroostook War remained bloodless when the Canadians and Americans, in the middle of a (“Mexican”) standoff, were inturrupted by a mother bear attacking the group nearest to her cub.
At the Battle of Tanga, the British Indian Army’s retreat from the East African Germans was turned into a route when the British stumbled over hives of angry bees.
In the animal vein: there is a story told that when, in 1349, Berne attacked the count of Gruyere (Switzerland), the women of the town of Gruyeres, who had taken refuge inside the city walls along with their livestock, had the idea of attaching torches to the horns of their goats and then herding the goats towards the attackers. The soldiers from Berne, frightened by this “attack from the devil’s army”, ran away. There is a mural in the castle of Gruyeres depicting the event.
For that matter, how about Louis Riel? Political or military leader?
To make up for the stunning lack of admirals on the lists, allow me to begin with several off the top of my head.
David Farragut
George Dewey
Raymond Spruance
Hyman Rickover (Yeah, he never fired a shot in anger. He also fought, and won, more political battles than I can shake a stick at.)
Daniel V. Gallery
Richard O’Kane
Isaac Hull
William Bainbridge
Thomas Truxtun
Some others who didn’t make flag rank:
Albert David
Charles ‘Swede’ Momsen.
James Lawrence (Though they did give up the ship, in spite of his dying words.)
Howard Gilmore (“Take her down.”)
Dudley “Mush” Morton
Donald “Kirby” Ross
JFK (For all that I believe the judgment of history vis-a-vis PT-109 is more complex than is usually acknowledged, he is still remembered for it.)
Jimmy Carter 
*In fairness to the OP’s restrictions, I have to confess that I often Googled to get the first names of some of my citations: Spruance, Lawrence, Dewey, Momsen, and several others are unique enough in my mind that I don’t think of them with first names. Though, where I have nicknames listed, those I knew.
Eh what about Crerar. The guy who as commander of the Canadian First Army in the Northern France campaign advanced the furtherest of any of the four allied armies while facing the most number of German troops*. Granted two of the three corps under his command were British, but he and Hodges were the best commanders that you could find in NW Europe in 1944-45.
Guy Simmonds his deputy took over for him during the Battle of theScheldt and pretty much destroyed the Germans in Belgium.
*Incidentally the commander who faced the least German formations and advanced the least was Patton, despite having 4 corps and something like 13 divisions under command.
Arthur Curry was probably Canada’s finest military commander. Apart from knocking off other peoples money here and there, he probably would be better remembered. (Also known as Currie).
I think Patton is just more of a popular hero. The Mike Wallace-hosted “Biography” series (1959-1961) on CBS devoted segments to Eisenhower, MacArthur, Nimitz, Halsey, Patton, Marshall (I think; been a while) but not Bradley, not Hap Arnold and not any other American officer of that war. Not that surprising, really. Take a guy like Audie Murphy; I’m sure he was unknown to anyone who didn’t know him during the war but now he is more famous than most guys who wore stars.
Hence the purpose of this thread: the Royal Navy has, for the better part of five hundred years, been the most important arm of the UK armed forces, but few Britons could name any admirals other than Nelson and Jellicoe (maybe), plus non-Admiral Francis Drake.
Interesting, I didn’t know about the Colditz connection - read Mark of the Lion, Reach for the Sky, and The Colditz Story as a kid, but can’t have connected the dots.
Perhaps we need a thread for military oddballs. 
Don’t forget Captain Morgan! 
Off the top of my head:
Shaka (Forged an empire out of scattered tribes, developed the Zulu military tactics that would give Imperial Britain a (brief) pause)
Jan Smuts (kicked British arse for a bit in the South African War, then helped saved it in two World Wars, helped found the RAF, the League of Nations and the UN, and invented the term “holistic”)
Sailor Malan (WWII flying ace, squadron leader, all-round good egg)
Koos De La Rey - guerilla commando leader
Argentina:
José Francisco de San Martin: He is our Washington. He fought in our revolutionary wars. He recognized early on that Argentina could never be truly free unless the Spanish were expelled from Chile and Peru… so he crossed the Andes (a feat of arms comparable with Hannibal’s crossing of the Alps), defeated the Royal Army and then invaded Peru.
Manuel Belgrano: Unlike San Martin, he wasn’t a professional soldier but a lawyer and an early economist. Despite that he was appointed commander of the Northern Army and was instrumental in defeating the Royal counter attack during our revolutionary wars.
Santiago de Liniers, Count of Buenos Aires: A french officer in the service of Spain, he defeated two English invasions to Buenos Aires. The people of Buenos Aires"elected" him Viceroy of River Plate and the king confirmed the appointment and made him Count Of Buenos Aires. The Marquis Of Sobremontes, Liniers predecessor is infamous.
William Brown: A native of Ireland who is the father of the Argentinian Navy.
Of course you all know General Lepoldo Galtieri
I always thought of him as more of a political leader
Belisarius was born in what today is Bulgaria but he was a Roman General. Bulgaria can’t claim him.
Try telling them that.
Incidentially, I wouldn’t call him Roman - the only thing “Roman” about him was the name of his country.
what about Paul Kruger?
Pretty much all Dutch cities have an area, built around 1900-10, where the streets are named after these guys from the Boer war. I lived in one of them, so most of these names are pretty familiar to me but really only as street names, not as actual political or military leaders. I think that if they were to decide whom to name those streets after they wouldn’t pick these guys anymore, though
Panama’s military leaders have mostly been ignominious.
The most famous has been Manuel Antonio Noriega, whose main military accomplishments were surpressing two coups against his rule and breaking up demonstrations with tear gas and water cannons. During the US invasion he showed exemplary leadership by immediately going into hiding and holing up in the Papal Embassy.
Omar Torrijos Herrera helped lead the coup against a democratically elected government that established the military regime in 1968.
Panama’s “War of Independence” from Colombia in 1903 was mostly non-violent. There was only one casualty, a Chinese shop-owner killed in his sleep by shelling by a Colombian gunboat. Gen. Esteban Huertas, head of the Colombian military garrison, became a Panamanian military hero when he permitted himself to be bought off by the revolutionary conspirators and sided with them when they declared independence. Placed in charge of the Panamanian army, he began to throw his weight around until the President fired him by disbanding the army in 1904.