Stretching firm and brand reputation

I consider an adverse selection model of product quality. Consumers observe the performance of the firm's products, and product performance is positively related to the firm's (privately observed) quality level. If a firm is to launch a new product, should it use the same name as its base product (reputation stretching), or should it create a new name (and start a new reputation history)? show that for a given level of past performance (reputation), firms stretch if and only if quality is sufficiently high. Stretching thus signals high quality.