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“fancy” in Latin

The English word fancy itself goes back to Latin phantasia, through fantasia.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

fancy
animus: sensus. (The words are found in this connection and order.) animus et sensus. [Vid: IMAGINATION.] ☞ Not phantasia, though it may be necessary to retain it as a technical term : *cogitationis luxuria or nimia quaedam ubertas. [Vid: IMAGINATION.] To have a lively fancy, acute moveri.
A fancy = an unfounded, wayward notion, somnium (dream): opinionis commentum: commentum mirum (strange fancy); in plur., ineptiae, nugae (nonsense, folly, etc.): cura inanis (a groundless anxiety). To take fancies, inanes species anxio animo figurare: *inanibus curis se dare (of gloomy fancies): away with your melancholy fancies, omitte tristitiam tuam: these are mere fancies, haec falsa et inania sunt: a foolish fancy occurred to me, ineptum aliquid mihi in mentem venit: to accommodate one’s self to anybody’s fancies, ad alicujus arbitrium or voluntatem se fingere, or se accommodare; se totum ad alicujus nutum et voluntatem convertere; totum se fingere et accommodare ad alicujus arbitrium et nutum: according to one’s own fancy, ad libidinem: ex libidine: to follow one’s fancies, animi impetum aequi (whatever impulse seizes one). [Vid: HUMOR.]
Inclination (for anything), Vid: To take a fancy for anything, libido me capit, libidinem habere in aliqua re (Sall., Cat., 7, 4): to have a fancy for doing anything, facere aliquid libido est (Plaut., Pers., 5, 2, 26): to take a violent fancy to do anything, magna (tanta, etc.) libido aliquid faciendi aliquem invadit (Sall.): to take a fancy for anybody, se inclinare ad (or in) aliquem (also aliquid); inclinatione voluntatis propendere in aliquem: a fancy for anybody, propensa in aliquem voluntas; propensum in aliquem studium: to have taken a fancy to anybody, propenso animo or propensa voluntate esse in aliquem: to have no fancy for anything, ab aliqua re alienum esse or abhorrere; nolle aliquid: to have no fancy either to... or, neque... neque... in animo est (Tac.).
FANCY GOODS, merces delicatae (Sen.). A shop for fancy goods, *taberna delicatarum mercium. A dealer infinitive. goods, *qui tabernam delicatarum mercium exercet: institor delicatarum mercium (as calling at the door with them; Sen., Ben., 6, 38, 3).
fancy v.
Imagine, etc., somniare (to dream): cogitatione sibi aliquid depingere (to picture it to one’s imagination): videri (seem): To fancy myself ill, *aegrotare mihi videor.
Like; have a mind to; Vid: LIKE; “am INCLINED to.

Quick answer

What is the Latin word for fancy?
The usual Latin words for “fancy” are animus, sentiō, moveō; also somnium, ineptia, nūgae. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.