There is a belief found in ancient China that as soon as words are made on paper - a corresponding material reality is a) generated, and/or b) reinforced (in the case of pre-existing realities). This sense of 'importance', 'inevitability' and 'mystery' stems from writing (a rare art right up to the 20th century in China) being associated with the ancient divination process.
Indeed, the Chinese writing system evolved from the shamans 'interpreting' and 'reading' the cracks made in collected turtle plastron and ox scapulae by the application of a hot poker. This followed a question being subnitted by the 'King' - which was carried-up to the divine-sky by the smoke generated by the hot poker 'touching' the shell or bone - with the (returning) answer being assumed to be contained in the subsequent 'cracks' that appeared! Needless to say, a body of knowledge (and associated 'interpretative' symbols) was eventually established.
Up until 1949 only around 10% of the Chinese population was 'literate' (with 90% remaining permanently 'illiterate') - with the 'literacy' rate today being in the high 90% (with 'illiteracy' remaining mostly amongst the very old or the cognitively disabled, etc) - but the cultural attitude toward the importance of 'words' still persists. Therefore, the naming of a martial art within Chinese-influenced cultures is rarely a trivial matter, and I suspect Miyagi Chojun had been thinking about - (and discussing this issue) - far more extensively (and in depth) than the usual 'naming' stories would suggest and imply.
When Miyagi Chojun chose the two traditional Chinese ideograms of '剛' (Go - Gang) and '柔' (Ju - Rou) he was achieving two objectives:
1) He was generating order in the material environment by 'confirming' the existential presence of his martial art. The art exists because the name exists - and vice versa. Within ancient China it was believed that by compiling lists of 'things' and 'objects' (including 'names') - a corresponding order was being constructed and reinforced in the material environment. An 'order' that cannot be questioned.
2) Miyagi Chojun was stamping his authority upon the art he had been taught and entrusted with by his teacher Higaonna Kanryo - projecting this order 'backwards' into history - all the way back through time (and associated 'lineage') to the 'root' of the art in Southern China. In other words, Miyagi Chojun was confirming the transmission and his receiving of the transmission - whilst proving he is worthy of it! He is placing his family's clan banner firmly in the ground, making a statement of authority and authenticity, and daring anyone to challenge him - which, of course - no one was stupid enough to do!
In this case, the martial art defined as 'Go' and 'Ju' had previously existed (in one form or another) - but now had reached a level of technical sophistication (and stabilization) so that the profound physical-psychological principles of 'Go' and 'Ju' (containing the corresponding meanings you ascribe) could now be considered fully established and developed!
Shifu Adrian Chan-Wyles (b. 1967) - Lineage (Generational) Inheritor of the Ch'an Dao Hakka Gongfu System.