Do you ask about a PowerCenter workflow or a workflow on the Informatica platform?
I only can respond for PowerCenter, hence this question.
In PowerCenter a relational connection pointing to an Oracle database can address this DB in two ways (which I know), namely either the TNS name (as defined in the TNSNAMES.ORA file) or by indicating the IP host name and port number directly (plus the DB service name), e.g. if the connect string is set up like this:
Other than that, I don't know of any methods.
Now the question is whether this connection is indeed of type Oracle or of type ODBC (which, although it should not be done, sometimes is used). If it's an ODBC connection, then you probably have chosen the wrong ODBC administrator to look up the Data Source Name.
There are two ODBC administrators on a Windows server machine, namely the 32-bit odbcad32.exe and the 64-bit odbcad32.exe. Both have the same file name, but they are located in different directory paths.
The 64-bit odbcad32.exe is by default stored in c:\Windows\System32\ .
The 32-bit odbcad32.exe is by default stored in c:\Windows\SysWOW64\ .
I dare to assume that the same replies hold true for the Informatica platform, but here a connection may be of type ODBC, JDBC, or Oracle, as far as I know, and I don't know how JDBC connect strings are set up in the platform.
Be aware you need to logon to the server which hosts the informatica processes to check for the odbc connection.
Client-tooling is using odbc connections which are on the machine hosting the client software hence you cannot try to take a look at the odbc connection using e.g. the Designer.
Additionally you need to look for a system DSN and not a user DSN since the windows user which runs the Informatica processes very likely differs from the account used to create the DSN.
Hope the information helps to solve your issue.