Terminology – Term for Nested Function Calls: func1(func2(), func3())

Using the word object in the reference is redundant.

Perhaps caller and callee is simplistic enough. Referring to the actual object as an instance of type is also another approach as noted by Wyatt; instance of Puppy or if being succinct is the goal...instance.

The term was adopted by computer scientists when they applied mathematical reasoning to programming in the mid 20th century.

The word argument has the general sense of something from which another thing may be deduced. It comes ‘from the L. arguere “make clear, make known, prove, declare, demonstrate,” from PIE *argu-yo-, from root *arg- “to shine, be white, bright, clear” ’, which root is also preserved in the words argent (“silvery white”) and Argentina (“[river] of silver”).¹

Its use in English to mean a “mathematical quantity from which another … quantity may be deduced, or on which its calculation depends” is attested as early as 1386:

 Argument (ā·ɹgiuměnt). [a. F. argument (13th c.), ad. L. argūment-um, f. arguěre (or refashioning, after this, of OF. arguement, f. arguer): see A_^RGUE. For use of the L. form, see 3 c.]
 2. Astr. and Math. The angle, arc, or other mathematical quantity, from which another required quantity may deduced, or on which its calculation depends.
 c 1386 C_^HAUCER Frankl. T. 549 Hise othere geeris, As been his centris and hise Argumentz.
 c 1391 — Astrol. xliv. 54 To knowe the mene mote and the argumentis of any planete.
 1796 H_^UTTON Math. Dict. I. 141/2 Annual argument of the moon’s apogee . . is the distance of the sun’s place from the place of the moon’s apogee.
 1879 T_^HOMPSON & T_^AIT Nat. Phil. I. 1. § 54 An arc of the circle referred to . . is the Argument of the harmonic motion.²