Hello, I've read a sentence as follow, 'In sentences with two complements the indirect object comes immediately after the verb (ie Brenda gave me a kiss); shoudn't it be the INDIRECT COMPLEMENT rather than INDIRECT OBJECT?
In other words, even though both 'me' and 'kiss' are the verb's complements, they are not called Indirect and direct COMPLIMEMTS but OBJECTS?'Object' is a well-established traditional term. 'Complement' is in more modern use, and covers various different grammatical roles, including objects:
Brenda kissed me. [This sentence has an object, which is one kind of complement.]
Brenda gave me a kiss. [This sentence has two objects, which are both complements, and which we distinguish as the indirect object and then the direct object.]
Brenda was elected president. [This is a subject complement, a different kind of complement. It equates Brenda = president]
Brenda considers me desirable. [Object complement, a different kind of complement. It equates me = desirable]
The term 'complement' is used for any grammatical role which is essential to the verb. It does not just mean 'object', which is one of the basic kinds of complement.
It is contrasted with other grammatical roles which you could just omit, such as 'on Tuesday' or 'in the kitchen' or 'slowly' or 'because I want to'. These are not complements.
Much obligedThese are just names. They're not important. They don't tell you important facts about the grammar. The usual name for 'me' in 'She have me a kiss' is the indirect object. That's just convention - grammarians choose to call it that. They could call it the aardvark object, or the banana complement. It would be the same thing. The grammar is the same. In describing English grammar, we don't use the term 'indirect complement'. We also don't use the term 'banana complement'.