You can, but beware. The Trade Marks Office will object to your application if your surname occurs on the Electoral Roll more than 750 times. Such names are deemed to be common and should be available for other traders with the same name. This is not a hard and fast rule and depends on the context of the goods.
Another factor to consider is whether your surname is also a geographical place name. That is also ground for objection to a trade mark application. Such an objection makes sense if a particular place has a reputation some obvious or potential connection with the goods or services.
As Gummow J stated at 503 in the Oxford case, the word "Oxford" was not inherently adapted to distinguish the applicant's books from those of other book publishers whose goods also emanated from Oxford:
The point is if goods of the kind in question are produced at the particular place or in the area, or if it is reasonable to suppose that such goods in the future will be produced there, other traders have a legitimate interest in using the geographical name to identify their goods, and it is this interest which is not to be supplanted by permitting any one trader to effect trade mark registration.
However, amateur Examiners often think that any place name, however obscure, is grounds for an objection.
For example, in the case of NATOWatchbands.com LLC [2021] ATMO 31 the Examiner objected to the place name BARTON on the grounds that it was a place in the Australian Capital Territory and 5100 had this surname in Australia.
Apparently Barton is world famous for Examiners in Canberra, but known to very few people outside of that area.
The fact that the Barton area was not known to have an obvious or potential connection to the goods, and the relatively small size of the location, was not enough to persuade the Hearing Officer that the objection was unwarranted. Evidently the Hearing Officer did not want to directly undermine the Examiner.
However, the Hearing Officer ultimately accepted the application on the basis of Nato's evidence of use of the trade mark for four years for watch bands and watch straps.
While Nato’s sales of the goods in Australia were not significant, they were successful in convincing the Hearing Officer that the anticipated sales and promotion of the trade mark were enough for registration – particularly because they would be able to participate in the Amazon Brand Registry once the Mark was registered, which would increase their sales in Australia.
The moral of the story is to steer away from surnames and place names when coming up with a new trade mark.