In this case, it helps to to a specialized search by limiting the types of results you are going to get or by adding other relevant keywords. In search engines you could try putting quotes around, such as "Speak Family" and limit the types of results. It may suite you more to search for specific names with other key words added, " 'Robert Speak' born in New York".
The most helpful I advice I can give you, however, is not to do search engine searches for the name "speak", but do search engine searches for specific resources, and then search for your name within those resources.
For example, you could do a search for "genealogy resources in New York" or "colonial families of rhode island" for example, and then from that list, FamilySearch might come up or a find-a-grave index. Go into those resource and then perform your search.
Another valuable option is to find a library in a bigger city and check out their genealogy department. You can do searches that will only include people's names, as they aren't going to bother indexing verbs. I hope this helps.