During our campaign this weekend we encountered an Ettin named Oinkers Boinkers. It had two heads (one head was Oinkers, the other was Boinkers), each with a different personality and it acted like two creatures in one body.

A sorcerer can twin a single-target spell to hit a second target that is different from the first target.

Legally, a basic Ettin is one target, I think, but the fact that I could say "I'm targeting Oinkers" or "I'm targeting Boinkers" suggests that there are two implied targets and a sorcerer could legally twin an attack spell to hit both heads but for their shared health pool.

Could a sorcerer act in this way?

Related: What qualifies for the target of a spell?

No, Twinned Spell requires two separate creatures

The Twinned Spell metamagic (PHB, p. 102) says:

When you cast a spell that targets only one creature and doesn’t have a range of self, you can spend a number of sorcery points equal to the spell’s level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).

An ettin is one creature; just because it has two heads, it does not count as two creatures, even if the creature has two heads, two separate names and two personalities. RAW, Twinned Spell would not allow a spell to target the ettin twice.

This is further supported by reading the description of the ettin in the Monster Manual (p. 132):

Dual Personality. The twin heads of an ettin are two individuals trapped in the same brutish body. Each head has its own mind, personality, and name, and possesses unique preferences and quirks.

...

When other creatures refer to an ettin, they combine its double names to form a single compound name that applies to the creature as a whole.