I am trying to have a minimum 3 characters of First Name and Last Name in order to retrieve the data, but now, it retrieves result of data even it is less than 3 characters.

Thanks in advance.

Bottom is Apex code:
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public with sharing class psw {
    public String sfprn { get; set; }
    public String mrn {get;set;}
    public String lname {get;set;}
    public String fname {get;set;}


public class TableRow2{
    public String sfprn {get;set;}
    public String mrn {get;set;}
    public String lname {get;set;}
    public String fname {get;set;}
    public Decimal SurveySelection {get;set;}
}

public List<TableRow2> RowList {get; set;}

public PageReference searchPatients(){

    RowList = new List<TableRow2>();
    TableRow2 tr;

    String bind_fname = string.isBlank(fName) ? null : (fname.left(3) + '%');
    String bind_lname = string.isBlank(lname) ? null : (lname.left(3) + '%');

    for(Patient__c con : [SELECT sfprn__c, 
                                mrn__c,
                                LName__c, 
                                FName__c,
                                (select SurveySelection__c.SurveySelection__c from SurveySelections__r) 
                                FROM Patient__c
                                where ( mrn__c =:mrn )
                              //or ( LName__c =:lname and FName__c =:fname) LIMIT 1 
                                or ( LName__c LIKE :bind_lname and FName__c LIKE :bind_fname ) LIMIT 1                       
                                ]){                                    
        tr = new TableRow2();
        tr.sfprn = con.sfprn__c;
        tr.mrn = con.mrn__c;
        tr.lname = con.LName__c;
        tr.fname = con.FName__c;
        tr.SurveySelection = con.SurveySelections__r.isEmpty() ? null : con.SurveySelections__r[0].SurveySelection__c;

        RowList.add(tr);         

        }
     return null;   
} 

}

Bottom is VF code:
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<apex:page Controller="psw" showHeader="false" sidebar="false">
<apex:form >
<apex:pageBlock >
    <!-- Search button-->
    <apex:pageBlockButtons location="top">
        <apex:commandButton value="Search" action="{!searchPatients}" reRender="contact-table"/>
    </apex:pageBlockButtons>

    <apex:pageBlockSection id="contact-table" columns="1">
        <!-- Input starts -->
        <apex:pageBlockSectionItem >
            <apex:outputLabel value="MRN" />
            <apex:inputText value="{!mrn}"/>            
        </apex:pageBlockSectionItem>

        <apex:pageBlockSectionItem >
            <apex:outputLabel value="Last Name" />
            <apex:inputText value="{!lname}"/>            
        </apex:pageBlockSectionItem>
        <apex:pageBlockSectionItem >
            <apex:outputLabel value="First Name" />
            <apex:inputText value="{!fname}"/>            
        </apex:pageBlockSectionItem> 
        <!-- Input ends -->

        <!-- Output 1 starts --->
        <apex:pageBlockTable value="{!RowList}" var="c">
            <apex:column >
                <apex:facet name="header">MRN</apex:facet>
                {!c.mrn}
            </apex:column>
            <apex:column >
                <apex:facet name="header">Last Name</apex:facet>
                {!c.lname}
            </apex:column>
            <apex:column >
                <apex:facet name="header">First Name</apex:facet>
                {!c.fname}
            </apex:column>                         
         </apex:pageBlockTable>
         <!-- Output 1 ends --->  
     </apex:pageBlockSection>       
    </apex:pageBlock>    
</apex:form>    
</apex:page>