Gov. Deval L. Patrick on Wednesday told about 100 supporters of gay rights that they have strong allies on Beacon Hill and that his administration is moving to improve state services for gay and lesbian youth. During an event at the Statehouse, Patrick, who has a lesbian daughter, Katherine, administered the oath of office to about 50 new and returning members of the Massachusetts Commission on Lesbian, Gay, Bisexual and Transgender Youth including two people from Western Massachusetts. The commission, created in 2006, is an independent state agency that recommends policies, programs and funding for gay youths in Massachusetts. "The work of affirming human dignity is never finished," the two-term Democratic governor told the crowd. "It's a journey."