I get the sense you are coming from a background in other programming languages. Immodestly, you might also want to look at this http://community.wolfram.com/groups/-/m/t/1167544 for general advice on querying data in Mathematica.
You can try with StringSplit and MemberQ:
StringSplit
MemberQ
zDataset = Dataset[zAssoc]; zDataset[Select[MemberQ[StringSplit[#Name], "Tom"] &]]