The word “savage” traces back to the Latin silva (forest or grove.) Although savage today means “wild” or “untamed” with overtones of ferocity or agression, it’s orginal meaning when applied to people was “indomitable” or “valiant.”
I once had a coworker whose last name was LeSavage. She said it was of Eastern European extraction, presumably anglicized (?) to its present form. I can see how it might have come from a Slavic name. This may be true of of many of the “Savages” we encounter.
“Savage” was a fairly common surname throughout Ireland in the mid-19th century. There were 673 Savage households in the Primary Valuation property survey of 1848-64. The Irish version is Sabhaois.
The verb “lynch” is relatively modern, named after Captain William Lynch of Virginia, who died in 1820. The Irish surname Lynch (Irish Ó Loingsigh) goes back centuries, and is from the Irish word loingseach, mariner.
Bit of a sidetrack, but I was watching a BBC show about the worst jobs in history and was surpirised where some (I thought) inoffensive surnames came from. Take Walker for example. It comes from an old tanning process where you got to walk in a vat full of urine and excrement to help the skins tan. I may never eat Walker’s crisps again!
A walker is a person who fulls cloth (fulling is the process of cleansing and thickening cloth by beating and washing). The “walker” walked on damp cloth to thicken it.