Meaning is certainly often involved when names are given (to children, or nicknames later in life); more or less depending on the culture -- European countries with a "foreign" religious tradition used to have "Christian" names deriving from Hebrew, Greek or Latin, the "original meaning" of which was totally unknown to most, or at best a matter of curiosity. Names simply recurred in families, skipping one or two generations; they reminded of the (great-)grandfather/mother more than they "meant" anything. Nowadays, especially among the least educated, babies are often named after the main characters of the last American movies / soap operas...
But even if a clear meaning is attached to a name (if only by popular etymology), it comes to mind only exceptionally. My wife is from the Middle East and she always knew her name means "wish," but that's not what she 'hears' every time her name is called. In normal usage a name stands for a face, a "person". And there must be a break, an interruption of this normal usage for the latent or potential 'meaning' behind the name to come front stage so to say. Indicated in speech by something like "that's why you were called X," "you were rightly/wrongly named," etc. Iow, even when the "meaning of a name" is transparent it can only be evoked by pun or wordplay structure, relating a functionally meaningless name to a meaningful noun, verb, etc. -- which is semantically distinct even though formally identical. And to this end, of course, a popular etymology works just as well as a "true meaning".
In Exodus 3:14 "I am" is 'hyh, not yhwh (no way Yhwh can mean "I am"; if it's construed as a verb it is a 3rd person). Moreover it is first part of a definite structure 'hyh 'shr 'hyh, "I am/will be that/who I am/will be" which had most likely a negative nuance, as in "who/what I am is none of your business" (cf. 33:19 for a similar structure and other negative responses in theophanies, Genesis 32:30; Judges 13:18), before it appears alone in 14b; the Greek translates egô eimi ho ôn, "I am the being = the one who is," and retains ho ôn, notegô eimi, as the isolated form. The absolute egô eimi of the Fourth Gospel are more directly reminiscent of Deutero-Isaiah (41:5; 43:10 etc.) than Exodus 3.