The built-in Gmail app does not support multiple signatures on individual accounts. However, it is possible to change the signature for each email account on your phone. Assuming you have multiple accounts (described in this guide), open the Email app and tap the Menu icon (three dots) at the top right, then select Settings.
From the Settings screen, tap on the account that you wish to change the signature of. On the account-specific settings screen, tap on the fourth row, entitled Signature. The following screen will present an edit box where you may create your signature. By using the Return key, you may create a new line – useful for separating various pieces of information.