I have seen foreign students with their name rendered phonetically in Kanji rather than katakana on their dogi/hakama. However, from what I've observed, the majority tend to render their names in katakana. Rendering one's name in Kanji makes it look more 'native' and fortunately, characters with nice meanings are chosen for the phonetic rendition
One problem with rendering the name in Kanji is that it may be open to different pronunciations... so unless the reader is relatively familiar with foreign names, she may not be clear on the intended name. Also, some Chinese surnames use characters not often seen in Japanese, so they can be a bit hard to read... My training partners have often asked me how to read the Kanji for my surname
On rendering place names in Kanji, I suspect it has something to do with familarity. Where I live, the English names for some places have been transcribed from the original Chinese names. In other words, the names of these places were originally written in Kanji. However, when Japanese living in this country write about those places in their community newspaper, they use the phonetic transcription, rather than Kanji. I guess it's because the Kanji names for these places are not well known outside the country (or by the Japanese living here) On the other hand, references to places like Taiwan or China are usually written using Kanji as these are more well known.
As to why I suggested kashira rather than atama... well... it sounds more artistic (also, one would tend to remember a name with a slightly unusual reading) As you know, kashira has a second meaning of group chief (the first meaning being the part of the body). So, taka no kashira has a double meaning - i.e. the head of the hawk and chief of hawks
On the other hand, atama tends to refer specifically to the physical body part or the mind.
I guess you may have to ask somebody like Akiyama san to tell us what he feels when he hears [taka no atama] and [taka no kashira]