The best indicator of a man's achievements during life are the locations of his portraits during death. Most die with a portrait hanging on the walls of the family house, or even worse: stuffed into an attic to gather dust, never to be seen again.
Or if you're someone like Gilderoy Lockhart, with a portrait hanging in the sitting room of every witch's home and down the halls of great institutions like The Order of Merlin and the Ministry of Magic. These people (like Lockhart) have been apt during life at stealing the credit of other great wizards and witches.
Others, like Fred Weasley, will find themselves flitting through portrait after portrait, each stop with a wonderful view of joke shops across the world. In life, Fred Weasley was a pain in the ass for teachers and other authority figures. In death, he was a pain in the ass for shoplifters and over-excited children.
Severus Snape was a different kind of man in life. Therefore he was a different kind of man in death. He died not a year after he succeeded the previous Headmaster of Hogwarts by killing him atop the Astronomy Tower. Hours after his death his portrait was installed in the new Headmistress' office.
There he would create rackets and complain constantly about trust-issues with Albus. He would get into heated arguments about blood purity with Phineas Nigellus Black. Minerva McGonagall would find herself completely unable to work in such situations, and she found herself in the staff room more often than not.
This earned Snape a portrait in the Slytherin Common Room, where he would be able to annoy Slytherin students rather than spend his time making noise in McGonagall's office. There, Snape would gleefully usurp the position of Head of House from Horace Slughorn. Students trusted him more, especially the temporary class of eighth-year students.
A year later his portrait was installed in the Halls of the Order of Merlin, Third Class. Snape would avoid that portrait like the plague. He couldn't stand to hear Gilderoy Lockhart yap about his wild achievements that in no circumstance could have been accomplished by even a powerful wizard in five lifetimes.
He even had a portrait installed in Malfoy Manor. In the years following Draco and Astoria's marriage, Snape would serve as a second father-figure to the youngest Malfoy, being there for Scorpius when Draco was too busy wallowing in his sorrow over mugs of firewhisky.
Snape was a special man in life, even if he didn't feel like it. He didn't deserve any of it, to be hung in McGonagall's office after only a year's tenure as Headmaster. He didn't feel like he deserved the posthumous Order of Merlin – who in their right mind gave him that after knowing he Sectumsempra'd a dead man's twin's ear off...or more importantly led to the deaths of Harry Potter's parents? (Lily Evans...)
He didn't deserve the portraits, Snape had thought. The only place he ever wanted to be was to be hung at a small cottage in Godric's Hallow. Snape dearly wished to have a portrait placed in the Potter family house and to share a wall with Lily Evans Potter.
His entire life had been devoted to Lily Potter. From the day they met and he scared off Petunia for her, through their increasingly shaky Hogwarts years, and during his tenure as Potions Master at Hogwarts – tasked to protect her son, Harry. Even his patronus was a doe, for Merlin's sake. More than that Potter can say for himself.
No, Snape didn't feel he deserved a space in the Headmistress' Office. Or an honorary title as Head of Slytherin House. Or placed in the halls of famous and accomplished wizards and witches in the Order of Merlin. He had never treated Draco well at school, much like how the Durselys spoiled their son Dudley. So he never understood why his portrait hung in Malfoy Manor.
He wanted only one thing, in life and in death, but he would never have it. And that was to share a wall with Lily Evans.