The rule-of-thumb test for whether or not you can use a particular name is "likelihood of confusion" among customers between the name you select, for the particular market you target, and names of existing companies also serving that market. If it is clear that customers should readily be able to tell the difference, and not get confused, it is generally safe to go with your proposed name (if in doubt, check with a knowledgeable lawyer).
With respect to any trade or service mark, even if registered as a federal mark, the scope of protection generally extends only to the particular "class" of goods or services for which the mark was registered. (See http://en.wikipedia.org/wiki/Trademark_classification for a general description of the classification system)
If a mark is particularly strong (e.g., Coke - fanciful, well-established, etc.), it can cut across all classes.
A classic case of an in-between mark, in which the holder contended that it was strong enough to cut across classes but lost in court on the issue, was the "Lexis" mark held by Mead Data, the legal research service. In the 1980s, Mead Data sued Toyota over its planned introduction of the "Lexus" brand automobile, claiming that customers would potentially confuse the marks. While Mead Data ultimately lost the case, the case went up through the court of appeals. (A summary of the dispute is found in this article: http://en.wikipedia.org/wiki/LexisNexis)
For most normal cases, marks will not be strong enough to cut across classes and it therefore is generally okay to use comparatively weaker marks in different fields with slight variations in the name (or often even with identical names, as long as they are in different jurisdictions).
Thus, the answer to your last question is generally "yes."