What is the proper term for a ternary digit?

A binary digit is a bit.

Is there an equivalent term for a three-state digit?

(e.g., a digit representing true, false, or unknown)

Trit.

At least, according to Wikipedia:

Analogous to a bit, a ternary digit is a trit (trinary digit)

I think that the question contains a faulty premise. There are many types of three-valued logic. Some three-valued systems include:

• A ternary numeral system, in which each digit is called a "trit" (short for TRinary digIT). Each trit can be 0, 1, or 2. The least-significant trit represents zero, one, or two; the second-least-significant trit represents three, six, or nine; and so on.
• A tri-state system, in which an electronic signal can have a high, low, or unasserted state.
• A nullable boolean, in which a variable can be true, false, or unknown/null. A sequence of nullable booleans doesn't represent any larger number; it works like a nullable bitfield.

I would therefore say that a "digit" representing true, false, unknown is not a digit at all, but rather a nullable boolean, or possibly a tri-state value.

Trit for trinary digit.
According to Princeton Wikipedia, since the Princeton article was retrieved from Wikipedia:

Analogous to a bit, a ternary digit is a trit (trinary digit). One trit contains log₂3 (about 1.58496) bits of information.

Trits and base 3 computing and hardware have been researched and developed in the 50's. The idea was to eliminate the 2 stage binary comparison by implementing the ternary logic less, equal, or greater outcomes or true, false, or unknown.

I was not able to find any published work with the definition of a trit, but a few articles talking about it and its implementation.
This is the closest to a definition given in American Scientist in an article about the third base:

Setun operated on numbers composed of 18 ternary digits, or trits, ...