Try this:

<?php
error_reporting(E_ALL);
$conn = odbc_connect("mssql", "login", "passwd",SQL_CUR_USE_ODBC);
var_dump($conn, odbc_errormsg($conn));
$query = "SELECT * FROM tablename";
$cur = odbc_exec($conn,$query);
var_dump(odbc_errormsg($conn));
echo odbc_cursor($cur);
var_dump(odbc_errormsg($conn));
?>

Thanks for responding. 

I tried your code as follow:

error_reporting(E_ALL);
$conn = odbc_connect("mssql", "login", "passwd",SQL_CUR_USE_ODBC);
var_dump($conn, odbc_errormsg($conn));
$query = "SELECT * FROM tablename";
$cur = odbc_exec($conn,$query);
var_dump(odbc_errormsg($conn));
echo odbc_cursor($cur);
var_dump(odbc_errormsg($conn));

Here is the result:
resource(16) of type (odbc link) string(0) "" string(0) "" string(0) ""

Could you try the attached patch?

According to the ODBC specification available at MSDN, then its possible for the SQLGetCursorName function to point to a NULL name where the length and return codes still are correct, so if thats the case it would fallback to the PHP cursor name which hopefully is the cause of this as I'm unable to reproduce it

patch failed to apply with the following error:
patching file php_odbc.c
Hunk #1 FAILED at 1470.
Hunk #2 succeeded at 1205 (offset -274 lines).
1 out of 2 hunks FAILED -- saving rejects to file php_odbc.c.rej

and from the php_odbc.c.rej file:
***************
*** 1470,1477 ****
        if (max_len > 0) {
                cursorname = emalloc(max_len + 1);
                rc = SQLGetCursorName(result->stmt,cursorname,(SQLSMALLINT)max_len,&len);
-               if (rc != SQL_SUCCESS && rc != SQL_SUCCESS_WITH_INFO) {
-                       char        state[6];     /* Not used */
                        SQLINTEGER  error;        /* Not used */
                        char        errormsg[SQL_MAX_MESSAGE_LENGTH];
                        SQLSMALLINT errormsgsize; /* Not used */
--- 1470,1477 ----
        if (max_len > 0) {
                cursorname = emalloc(max_len + 1);
                rc = SQLGetCursorName(result->stmt,cursorname,(SQLSMALLINT)max_len,&len);
+               if ((rc != SQL_SUCCESS && rc != SQL_SUCCESS_WITH_INFO) || !cursorname) {
+                       char        state[6];
                        SQLINTEGER  error;        /* Not used */
                        char        errormsg[SQL_MAX_MESSAGE_LENGTH];
                        SQLSMALLINT errormsgsize; /* Not used */

Does this apply to 5.3 too?

No feedback was provided. The bug is being suspended because
we assume that you are no longer experiencing the problem.
If this is not the case and you are able to provide the
information that was requested earlier, please do so and
change the status of the bug back to "Open". Thank you.

Yes, This apply to PHP 5.3.18 and also 5.4.8.