If I can't copy the name, might I imitate the ‘look and feel’?

The trademark laws may protect distinctive elements of design, decorative or non-functional aspects of a business under the concept of "trade dress". The United States Supreme Court has dealt with this issue on several occasions. Protection is indeed available, but the protectable trade dress must be "nonfunctional" and must have achieved “secondary meaning.” These concepts are often difficult to apply, which is why advice from a trademark lawyer on the particular facts you have in mind is so important.
 

What part of a trademark is protected?
Under the Lanham Act, all of a product’s packaging is protected under trademark law. There are two distinct parts to a trademarked package. The first is the name itself. This includes the font, color, size, and aspect ratios as well as the actual words that are used. For instance, the computer company Hewlett Packard has the trademarked letters “hp” to represent their products. Along with the letters themselves, they are italicized and both lowercase. All of those aspects are protected under the function part of the trademark laws.

The Lanham Act also protects non-functional trademark designs. Going back to the above example, the “hp” are positioned in the center of a rectangle and a circle. While the rectangle and circle do not actually communicate anything, they are associated with the brand, and when people see the symbol, they automatically think of Hewlett Packard.

What does trademark law specifically protect against?

That Landham Act was an effort on the parts of its creators to leave absolutely no wiggle room. The law specifically states that:

Any person who, on or in connection with any goods or services [...] uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which

(A) is likely to cause confusion, or to cause mistake, or to deceive [...] as to the origin, sponsorship, or approval of his or her goods, services, or commercial activities by another person, or

(B) in commercial advertising or promotion, misrepresents the nature, characteristics, qualities, or geographic origin of his or her or another person’s goods, services, or commercial activities,

shall be liable in a civil action by any person who believes that he or she is likely to be damaged by such an act." 15 USC Section 1125


In other words, you may not even create a trademark with the same feel of another existing trademark if it will cause confusion to consumers. If you are unsure whether your proposed trademark is in violation of federal law, consult with an intellectual property attorney.