A man can not change his gothram, per definition of it. Gothram represents the passing down of 'Y' Chromosome from one of the original rishis through the males (females do not carry this chromosome).
As Sri Ramachandran Ji pointed out elsewhere, males through their sperms give 'soul' to a person as the mother's egg only provides for physical body (this is the belief). So, gothram is identified for the males to worship one's forefathers who have given us the 'souls'. Again this is the belief.
Sir,
I have actuallly been wondering why did this belief come up (of women not giving 'soul' to the child, being silent spectator in creation, and so on) for quite some time now. Honestly, it still does not make sense to me (since both a man and woman play an equal role in 'creating life'). Only wish we had a system where men and women are both considered equally important to a child (just in case it is not considered that way).
What i have been thinking is that 'perhaps' the male pithrus need to be appeased because there are many more y-chromosome linked mutations passed on as diseases than x-linked ones (which in fact are few, 'mothers' seem to be fairly harmless in the survival scenario). Men in fact are supposedly the weaker sex in terms of being prone to a lot more health conditions than women. And perhaps that is why the male side needs to be 'worshipped', to placate 'it', appease 'it', so that some divinity or 'modificational energy' is invoked to ensure healthy generations.
I was also talking to one monk asking him why villages are gothrams for some people. He said that in the old times branches of rishi gothras started being named after a prominent person, like someone who established a branch of the same people in an other place. This was to accomodate growth in population. When populations grew, many sub-branches, sub-sub-branches and further divisions kept getting established. By this time, people had spread out in 'far off' places.
When numbers grew even more, and people branched away further, villages started being used to identify a branch (since the branches wud create and settle in new villages, the village names became an identifier). Naturally everyone in the village wud not be doing same occupation, but they wud be the same gothra. Over time many people in various occupations forgot their gothras, except the ones that needed to remember it or mention it during prayers. It was for this reason, that when people reverted to hindu after being buddhist or jain, they took on village names as gothras, since that was acceptable in hindusim at that time as a gotra branch identifier. Therefore one sees all kinds of gotras being mentioned during archanai (like names of rishis, names of gods like Shiva and Vishnu, some ancestor names, village names, etc as a gothras).
Methinks this whole idea of using village names is common in the old southindian names, not seen in the north. Many northies also do not have gothras (while performing a homam, it is common for a priest to mention his own gothra or give his own gothra to the client, since many northies were filled in as the 'kshatriya' group). So it maybe possible that this old gotra system, as mentioned by the monk, was created and followed in southindia or by people who later came to be called southern-indians.
It may also be possible that a section of the northies were actually matrilineal tribes (among some punjabis the mother whispers the name of the child into the baby's ear thrice during namakaranam, not the father); though they are actually considered patrilineal people (did this crossing over of becoming patrilineal happen in the puranic times ?). Also many southies do have a village name affixed to their name but profess non-village gothras like vashista, vishwamitra, kashyapa, etc...probably this too happened in the puranic times..its like old wine filled in a new bottle or like naming a child back again after one of his ancestors after 2k generations perhaps.
Anyways, all this is based on conversations with a guru. I have no way to autheticate it.