As defined in the custom fields edit form, the field short name is case-sensitive and it is validated and cleaned as PARAM_ALPHANUM using the expression: preg_replace('/[^A-Za-z0-9]/i'
So, are valid short names any of:
foo
Foo
1foo

This has several side effects:

1) short names are saved in the user_info_field table verbatim, but are often compared in a case-insensitive way, e.g. grade_helper::get_user_profile_fields() fragment

        $customprofilefields = array_map('trim', explode(',', $CFG->grade_export_customprofilefields));

		...

			foreach ($customfields as $field) {

                // Make sure we can display this custom field

                if (!in_array($field->shortname, $customprofilefields)) {

works properly only when char-cases matchs.

2) as result, these produces inconsistent behaviours, as reported e.g. MDL-44982, MDL-38129, MDL-41145, etc... Moreover, changing a short name from upper- to lowercase, cause attribute mapping in db, LDAP and SSO authentication goes messy

3) a minor annoyance: in many point, short names are used as object property names, e.g.: auth_plugin_base::get_custom_user_profile_fields()

	$this->customfields[] = 'profile_field_'.$proffield->shortname;

Even if in this case it works properly, it can lead to some difficulty if someone have to access a specific custom field directly (e.g. a plugin or https://moodle.org/mod/forum/discuss.php?d=91370) because PHP variable/property names cannot start with a number, thus
$proffield->1foo
is invalid.

Proposed solution: add a new param type PARAM_FIELDNAME with this behaviour:

        case PARAM_FIELDNAME:

            // Remove everything not `a-zA-Z0-9`.

            $param =  preg_replace('/[^A-Za-z0-9]/i', '', $param);

			return strtolower(preg_replace('/^[0-9]+/', '', $param));

and use it in profile_define_base::define_form_common()
Add a similar param type PARAM_FIELDNAME_LIST:

        case PARAM_FIELDNAME_LIST:

            $params = array();

			foreach (explode(',', $param) as $fieldname) {

				$fieldname = preg_replace('/[^A-Za-z0-9]/i', '', $fieldname);

				if ($fieldname) {

					$params[] = strtolower($fieldname);

				}

			}

			return implode(',', params);

and use it everywhere field name list occours, such as in grades.php

Impact: no impact on new defined custom fields, possibly configuration breaks when an existing custom field is edited