Of course hats, wrists bands, arm bands, headbands and other accessories are acceptable as long as they do not put the player in harms way. Commercial brands or name brands are alright but not really essential. As long as they serve their purpose of keeping the tennis player comfortable it does not really matter if it's a famous brand or not.
Now that we have a clearer idea on what is the composition of the proper tennis apparel we can now move into where to look for them. The tricky part of looking for where to buy your tennis apparel is whether you go for a name brand (commercial brand) or not. There are pros and cons to whichever choice but ultimately it is still the player who decides. When looking for a place to buy your tennis apparel always keep some things in mind.
First is the reputation of the store or the shop. If the store has a reputation of selling low quality goods then you may need to look for another one. Another consideration is where your friend or peer buys their apparel. Ask other people for recommendations, as it is one of the best ways to find a good store.
Another thing to keep in mind is the number of clients that are players of the sport as well. If there are other players who are buying from a certain store or shop then that place may have some things that the others don't that attract a large number of consumers to their store.