Q: How close does the look and feel of a logo or name have to be for it to constitute trademark infringement?

A: The standard for trademark infringement is called "confusingly similar," meaning that a mark must be confusingly similar to an ordinary person in the marketplace for the goods. Here is a good discussion on the standard found in the wikipedia page for "confusing similarity"

Where mark X is not identical to a registered trademark, the use of mark X may still amount to an infringement if it is "confusingly similar" to the registered trademark. Mark X may share elements of spelling or style that would lead a reasonable observer to believe the trademarks were related.

For example, in the computer industry, Microsoft has become such a well known trade name and trade mark that other businesses in the industry may want to use the term "micro" or "soft" in their names. As Microsoft generally does not hold exclusive rights in these terms, it would need to establish that any trade names or trademarks which include these terms is confusingly similar to "Microsoft". The reputation attaching to a trademark is also significant, such that "Microsafe" or "Micro Software", although clearly not identical, could potentially be confusingly similar and amount to an infringement.

In addition, the style of a trade mark, such as a logo or font, can become relevant. For example, Microsoft products are distinguished in the marketplace by a consistent font. Competitors may not use the same font on their product, particularly when using a name which would not be confusingly similar except for the use of the font. For example, a brand called "Microsystems" would most likely not be confused with Microsoft. However if Microsystems used the same font as Microsoft, it would be confusingly similar. Some styles, like the script used on Coca-Cola products, are so well known that even a completely different name in a similar script could be held to be confusingly similar.

Cases of this type can be proven by using surveys which show that members of the public who are likely to use the services or goods protected by the trade mark have been confused by it. However, courts can also take judicial notice that an infringing mark is confusingly similar if it is obvious to even a casual observer.

https://en.wikipedia.org/wiki/Confusing_similarity