There is no requirement as to which of a player's available transporters are to be used - if the transporter with one ring is in use and a new ship is built, the player may choose whether the newly built ship becomes the player's first ship (by choosing the transporter with no rings) or whether the existing ship retains the first ship designation (by choosing the transporter with two rings).
Players have no requirement to utilize a specific transporter when constructing new ships. If one transporter has one ring and is currently in use, players can decide whether their newly built ship becomes the primary vessel by selecting the transporter without rings or keep the existing ship as the first ship by choosing the transporter with two rings.