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I wonder if the German/Dutch/Danish/etc surname (and variants) 'Theil' (ala Henri Theil), 'Theile', 'Thiel', 'Thiele' 'Thile' (ala Chris Thile) et cetra, have their etymologic roots from this ancient Germanic profession.
There are some sources  where etymologies are given that attest to "Theil" in German, being related as an archaic version of the modern German 'teil' with a different meaning more akin to a possible cognate of the modern English "deal" (as in, to be "dealt"; given, 'expelled' with some conveyance of 'imparted'; as in a 'teller', one who shares information). c.f.
"From the Anglo-Saxon ordael or ordela (from or=ur, and dael=theil): German: Urtheil or Gottesurtheil; Dutch: oordeel; French: ordéal; L. Lat.; ordalium, ordale, ordela. See Du Cange sub. ordela, aquae frigidae judicium, Duellum, Ferrum candens; Skeat (Etymol. Dict. of the Engl. Lang.) sub. Deal."
"O.E. ordel, lit. "judgment, verdict," from P.Gmc. noun *uzdailjam (cf. O.Fris. urdel, Du. oordeel, Ger. urteil "judgment"), lit. "that which is dealt out" (by the gods), from *uzdailijan "share out," related to O.E. adÊlan "to deal out" (see deal). The notion is of the kind of arduous physical test (such as walking blindfolded and barefoot between red-hot plowshares) that was believed to determine a person's guilt or innocence by immediate judgment of the deity, an ancient Teutonic mode of trial. Eng. retains a more exact sense of the word; its cognates in Ger., etc., have been generalized. Curiously absent in M.E., and perhaps reborrowed 16c. from M.L. or M.Fr., which got it from Gmc. Metaphoric extension to "anything which tests character or endurance" is attested from 1658. The prefix or- survives in Eng. only in this word, but was common in O.E. and other Gmc. languages (Goth. ur-, O.N. or-, etc.) and was originally an adv. and prep. meaning "out.""
In the etymology for "teller" from the same site;
"Origin: bef. 900; ME tellen, OE tellan to relate, count; c. D tellen to reckon, count, ON telja to count, say, OHG zellén; akin to tale"
Thus possibly an association to the German 'teil' or 'part'/'section'; i.e. from "count", count out; to "recount" deeds. etc... "deal";
"Origin: bef. 900; (v.) ME delen, OE dǣlan (c. G teilen), deriv. of dǣl part (c. G Teil); (n.) in part deriv. of the v.; (in defs. 19 and 23) ME deel, del(e), OE dǣl" Nagelfar 12:16, 10 March 2007 (UTC)