In Act V of Shakespeare's ANTONY & CLEOPATRA, the character Dolabella
says to Cleopatra, "Assuredly you know me."  How would she if
nowhere in the play have they met nor has anyone spoken to her of him?

Perhaps Dolabella assumes that Caesar would have spoken of him to
Cleopatra, and that Cleopatra would thus know something of him.

I agree with Pinkfreud. This is not my area of knowledge but perhaps
this narrative form of the play may help you.
Shakespeare Stories II (Hardcover) by Leon Garfield.
 http://www.amazon.com/exec/obidos/ASIN/0395708931/amzna9-1-20/ref=nosim/104-6911645-8228708?dev-t=D26XECQVNV6NDQ%26camp=2025%26link_code=xm2

Bear in mind that Dolabella is one of Octavius Caesar?s men (also
described as a friend of Octavius), so from this narrative perhaps he
believes Cleopatra would have been told of him.

Page 88. 

"Dolabella bowed courteously. He had come to prepare the way for his
master. ?Most noble empress, you have heard of me??
?I cannot tell?
Dolabella was surprised. He was a person of some importance.
?Assuredly you know me.?  "


http://www.sparknotes.com/shakespeare/antony/characters.html
http://www.gradesaver.com/classicnotes/titles/cleopatra/charlist.html

Thank you both, this info is helpful.  But has Caesar met with Cleo
previously?  In the text when Caesar arrives at the monument he asks,
"Which is the queen of Egypt?"

Well, Antony should know all the intimates of Caesar and perhaps
Dolabella assumes that Antony has briefed her on the political cadre
she is facing and they are fighting.
Up to this point Octavius and Cleopatra have not met face to face and
the fact that she kneels at his entrance (something royalty would not
ordinarily do) along with her servants and attendants leads to his
confusion.