I have Sole Custody and Guardianship of my 3 year old daughter. Can I change her surname even if the biological father does not give me his consent? The father has "reasonable access" to my daughter, and that's all. I live in B.C, Canada.

I am not sure exactly where you are but here is some information for Ontario:
FORMAL NAME CHANGE – CHILD (Under 18) - Health social services - Gateway Individuals - Government of Ontario (Canada) (http://www.gov.on.ca/ont/portal/!ut/p/.cmd/cs/.ce/7_0_A/.s/7_0_252/_s.7_0_A/7_0_252/_l/en?docid=119598)
Besides giving instructions on how to do it, it basically says this at the bottom: A note about custody & access: If you have sole custody, others may still be entitled to legal access to the child. If a court order is silent on the issue of access, you will be required to provide notice of the proposed name change to persons who might otherwise be entitled to legal access to the child (e.g. a parent who is named on the child's birth registration but does not have custody of the child).
Hope that helps.

Sorry I see now that you did say where you are so if you haven't found it yet yourself here is info for B.C.:
BC Vital Statistics Agency - Who is eligible to change a name? (http://www.vs.gov.bc.ca/name/eligible.html)
And specifically in regards to getting the court to waive the others persons consent:
BC Vital Statistics Agency - Waiver of Parent's Consent for Legal Name Change (http://www.vs.gov.bc.ca/name/waiver.html)