Let me suggest to you to aim for consistency.
Secondly, in databases like the above mentioned (and Thomson Reuter's Web of Science, to mention another, aiming less on engineering than Scopus), you may search for researchers by family name and initial of the given name; however I personally find it more straightforward to narrow the research by knowing the complete given name, than guessing if "Doe, B" refers only to "Doe, Bill" or / and "Doe, Benjamin", "Doe, Barry" I would prefer the same for the middle name (if existing).
For the databases like Thomson Reuters' Web of Science, or Elsevier's Scopus, or Scifinder Scholar (by the American Chemical Society), these databases do not mind terribly much how much of the middle name of the authors is provided. Either one finds you and your publications taking into account field of research, or affiliation to a group as additional criteria while doing the literature search the classical way. Or, while launching a query based on the alpha-numerical badges (ResearcherID, ScopusID, Orcid), because these publications are associated with you, because you taught the database that the publication in question actually is one you ("Doe, Benjamin") contributed to, and not "Doe, Bill".
As a side note to the second paragraph, if you manage your publication record with ResearcherID, you may sychronise these entries with Orcid (and the other way around, too). Web of Science even lists both the own ResearcherID and Orcid in its abstracts, where available. Likely, such a link may be established to Scopus, too; hence this work needn't be done each time from scratch for every database in question.
