Is it legal to build a computer by assembling all the components needed and sell the pocket sized computer under a new name?

Yes, unless someone else already did the same thing and obtained a patent on the new device. Likewise, you cannot adopt a new name for the product if that name would be confused with an existing name of the same or a similar device.

Yes but you had better make sure that you are buying these components from a licensed retailer and that they are not sold under a "Not For Resale" agreement. Also I would make sure that none of the products you are buying infringe anyone else's IP rights.

If the computer you are building and selling is protected by a patent then you may be infringing the patent by building the computer. The name of the computer would probably not be relevant.

If you are creating an entirely new product, your proposal would be legal. However, if you are copying most or all of an existing system that is protected by a patent and you don't have a license to do so, you would be infringing the patent or patents and would be liable in federal court for any damages caused to the patent holder/holders. If you've been following patent news lately, you'll already know how pricey patent violations can be.