I have a Rem VLS .308 win with a Leo scope I got as a "pro form" while I worked at Garts sports. Leopold offered to engrave my name on it but I knew whos scope it was so I had them engrave "Die Verbindung" which is pronounced "dee vairbeendung" which means "the connector" or "that which brings together" so the gun is "The Connector."
I also have a Win 1300 12 gauge shotgun with a folding stock and mag that sticks out 3" in front of the 18" bbl with a side saddle ammo mount and pistol grip front and rear. The family calls it "Mr. Yuck"
The stainless mini 14 (slightly "brightened" bbl and trigger than when it came from the factory) is simply known as "Moms rifle" because she likes to shoot it so much.
My favorite rifle came with a name. When I was 18 my grandpa gave me his Winchester Mod 70 pre-64' in 30-06. The most prized rifle I have, for obvious reasons. Anyhow he called it: