In a similar situation, not a baby name/blessing but blessing a sick baby, President Joseph Fielding Smith said:
"Does a wife hold the priesthood with her husband, and may she lay hands on the sick with him, with authority? A wife does not hold the priesthood with her husband, but she enjoys the benefits thereof with him; and if she is requested to lay hands on the sick with him, she may do so with perfect propriety."
When this is done the wife is adding her faith to the administration of her husband. The wife would lay on hands just as would a member of the Aaronic Priesthood, or a faithful brother without the Priesthood, she in this manner giving support by faith to the ordinance performed by her husband. (Doctrines of Salvation, comp. Bruce R. McConkie, 3 vols. [Salt Lake City: Bookcraft, 1954-56], 3:177.)