In swift 2.0 this can be done as follows
//Defining fonts of size and type
let firstfont:UIFont = UIFont(name: "Helvetica Neue", size: 17)!
let boldFont:UIFont = UIFont(name: "HelveticaNeue-Bold", size: 17)!
let thirdFont:UIFont = UIFont(name: "HelveticaNeue-ThinItalic", size: 17)!
//Making dictionaries of fonts that will be passed as an attribute        
let firstDict:NSDictionary = NSDictionary(object: firstfont, forKey:  
NSFontAttributeName)
let boldDict:NSDictionary = NSDictionary(object: boldFont, forKey: 
NSFontAttributeName)
let thirdDict:NSDictionary = NSDictionary(object: thirdFont, forKey: 
NSFontAttributeName)
let firstText = "My name is "
let attributedString = NSMutableAttributedString(string: firstText, 
attributes: firstDict as? [String : AnyObject])
let boldText  = "Rajan"
let boldString = NSMutableAttributedString(string:boldText, 
attributes:boldDict as? [String : AnyObject])
let finalText = " iOS"
let finalAttributedString =  NSMutableAttributedString(string: 
finalText, attributes: thirdDict as? [String : AnyObject])
attributedString.appendAttributedString(boldString)
attributedString.appendAttributedString(finalAttributedString)
myLabel.attributedText = attributedString
Edit 
 Swift 3.0
let firstfont:UIFont = UIFont(name: "Helvetica Neue", size: 17)!
let boldFont:UIFont = UIFont(name: "HelveticaNeue-Bold", size: 17)!
let thirdFont:UIFont = UIFont(name: "HelveticaNeue-ThinItalic", size: 17)!
//Making dictionaries of fonts that will be passed as an attribute
let firstDict:NSDictionary = NSDictionary(object: firstfont, forKey:
        NSFontAttributeName as NSCopying)
let boldDict:NSDictionary = NSDictionary(object: boldFont, forKey:
        NSFontAttributeName as NSCopying)
let thirdDict:NSDictionary = NSDictionary(object: thirdFont, forKey:
        NSFontAttributeName as NSCopying)
let firstText = "My name is "
let attributedString = NSMutableAttributedString(string: firstText,
                                                     attributes: firstDict as? [String : AnyObject])
let boldText  = "Rajan"
let boldString = NSMutableAttributedString(string:boldText,
                                               attributes:boldDict as? [String : AnyObject])
let finalText = " iOS"
let finalAttributedString =  NSMutableAttributedString(string:
        finalText, attributes: thirdDict as? [String : AnyObject])
attributedString.append(boldString)
attributedString.append(finalAttributedString)
myLabel.attributedText = attributedString
Edit 
 Swift 4.0
let firstfont:UIFont = UIFont(name: "Helvetica Neue", size: 17)!
let boldFont:UIFont = UIFont(name: "HelveticaNeue-Bold", size: 17)!
let thirdFont:UIFont = UIFont(name: "HelveticaNeue-ThinItalic", size: 17)!
//Making dictionaries of fonts that will be passed as an attribute
let firstDict:NSDictionary = NSDictionary(object: firstfont, forKey:
    NSAttributedString.Key.font as NSCopying)
let boldDict:NSDictionary = NSDictionary(object: boldFont, forKey:
    NSAttributedString.Key.font as NSCopying)
let thirdDict:NSDictionary = NSDictionary(object: thirdFont, forKey:
    NSAttributedString.Key.font as NSCopying)
let firstText = "My name is "
let attributedString = NSMutableAttributedString(string: firstText,
                                                         attributes: firstDict as? [NSAttributedString.Key : Any])
let boldText  = "Rajan"
let boldString = NSMutableAttributedString(string:boldText,
                                                   attributes:boldDict as? [NSAttributedString.Key : Any])
let finalText = " iOS"
let finalAttributedString =  NSMutableAttributedString(string:
    finalText, attributes: thirdDict as? [NSAttributedString.Key : Any])
attributedString.append(boldString)
attributedString.append(finalAttributedString)
myLabel.attributedText = attributedString
This will look like
