It is rare for the taking of an oath itself to cause controversy. In the UK the only real controversy resulting from oath-taking is the long-standing refusal of members of Sinn Fein to swear the oath of allegiance to the queen to take their seats in the House of Commons - though the suspicion is that even if the oath requirement were waived they still would not take those seats much as they did not take their seats in the Irish Dail until the 1980's as this meant recognising Northern Ireland's constitutional status.
In Hong Kong, however, this ordinarily straight-forward process has become the source of a great controversy. Baggio Leung and Yau Wai-ching, newly elected to the LegCo seats for New Territories East and Kowloon West, both attempted to make oaths firstly to "the Hong Kong nation". Yau Wai-ching then went on to call the People's Republic of China the "People’s Re&*^%ing of Chee-na".
Believe it or not, but the part of this that appears to have caused the most offense was the description of China as "Chee-na" (支那 or "Zhi Na" in Hanyu Pinyin). Whilst this term might appear to be just another version of the term "China", and indeed comes from the same root, it taps into memories of (and more importantly, memories of education about) the so-called "Century of Humiliation". The logic is that, as this term was used for China by the Japanese ("Shina" in Japanese) to belittle China (or at least, avoid calling it the rather self-aggrandising name meaning literally "Middle Country" under which it presently goes) during the period during which the Japanese carried out a ruthless and brutal invasion of China, then the term "Shina" (and any other version of it) is itself offensive.
Personally I avoid using terms I think might offend people even if I'm dubious about the logic under which it is supposed to be offensive, if using the term is reasonably avoidable. I would never use the term "Zhi Na" and think that using it to essentially rile the pro-Beijing camp was basically a childish and stupid act. You regularly see Japanese nationalists and others using the term "Shina" simply because they wish to cause offence, and Yau Wai-ching's acts were in the same vein. That the Pro-Beijing camp has now over-reacted in a fashion that, to people on the pan-democrat side in Hong Kong, shows what faux-nationalist puppets of Beijing they are and given HK localists a massive publicity coup beyond anything they could have achieved simply by taking their seats, does not justify what was done.
All the same it is pretty obvious that that there is ultimately little difference between "Shina" and the name "China" itself - "China" is also a name that we English-speakers use for the country currently ruled by the Chinese Communist Party at least partly because a literal translation of the Chinese name for that country sounds ridiculously self-aggrandising and quaint, and was also the name used for China during the Opium Wars and later. However, few suggest that we should use the term "Middle Country" or "Middle Kingdom" for China* instead of the name we presently use - although I would not at all be surprised if this happens in the future.
*The name "Great Britain" is sometimes brought up in these circumstances, but this is a misunderstanding: "Great" here merely indicates the largest island of the British isles.